The idea that Catholics can believe in evolution is not only from Pope John Paul II saying that the Church accepts eviloution, but it goes back to the 1950 encyclical by Pope Pius XII. Before I continue with the modern belief that Catholics hold, I feel its best to just provide a little history on the topic.
-Pre Vatican II & Pope Pius XII-
Pope Pius XII's encyclical
Humani Generis, holds a neural possition in regards to evioultion. "The Church does not forbid that...research and discussions, on the part of men experienced in both fields, take place with regard to the doctrine of evolution, in as far as it inquires into the origin of the human body as coming from pre-existent and living matter." (Pope Pius XII, encyclical
Humani Generis).
"Now it is in no way apparent how such an opinion (polygenism) can be reconciled with that which the sources of revealed truth and the documents of the Teaching Authority of the Church propose with regard to original sin, which proceeds from a sin actually committed by an individual Adam and which, through generation, is passed on to all and is in everyone as his own." (Pius XII, Humani Generis, 37 and footnote refers to Romans 5:12-19; Council of Trent, Session V, Canons 1-4)
Pope Pius XII's statement can be summarized as the following:
1. The question of the origin of man's body from a pre-existing and living matter is a legitimate matter of inquirty for natural science. Catholics are free to form their own opinions, but they should do so cautiously; they should not confuse fact with conjecture, and they should respect the Church's right to define matters touching on Revelation.
2. Catholics
must believe that the human soul was created immediately by God. Since the soul is a spiritual substance it is not brought into being though transformation of matter, but directly by God, whence the special uniqueness of each person.
3. All men have descended from an individual, Adam, who has transmitted original sin to all man kind. Catholics may not, therefore believe in "polygenism".
-Post Vatican II & Pope John Paul II-
Flash forward to Vatican II and the years after that. Modern theologians dont necesarily see a conlict between polygenism and the Catholic teaching on original sin while some disagreed. It was on October 22, 1996 that Pope John Paul II made his address to the Pontifical Academy of Science and updated the Church's position to accept evolution of the human body, however in the same address the late Pope rejected any theory of evolution
that provides a materialistic explanation for the human soul.
"In his encyclical Humani Generis (1950), my predecessor Pius XII has already affirmed that there is no conflict between evolution and the doctrine of the faith regarding man and his vocation, provided that we do not lose sight of certain fixed points....Today, more than a half-century after the appearance of that encyclical, some new findings lead us toward the recognition of evolution as more than an hypothesis. In fact it is remarkable that this theory has had progressively greater influence on the spirit of researchers, following a series of discoveries in different scholarly disciplines. The convergence in the results of these independent studies -- which was neither planned nor sought -- constitutes in itself a significant argument in favor of the theory.
Theories of evolution which, because of the philosophies which inspire them, regard the spirit either as emerging from the forces of living matter, or as a simple epiphenomenon of that matter, are incompatible with the truth about man." (John Paul II, Message to the Pontifical Academy of Sciences on Evolution)
More in detail on John Paul II's Message to the Pontifical Academy of Science on Evolution
-Pope Benedict XVI-
In the Papacy of Benedict XVI, recent statements by Cardinal Schonborn has lead confusion over the Church's stance on the compatibility between evolution and Catholic Dogma. After learning the lessons learned from the Galileo affairs, the Church leaves the evaluation and endorsements of specific scientific theories to scientists. The Church has always agreed with scientists on matters such as the age of the Earth and the authenticity of fossil records. Pope Benedict XVI (Then Cardinal Ratzinger at the time when adding this statement) stated;
According to the widely accepted scientific account, the universe erupted 15 billion years ago in an explosion called the 'Big Bang' and has been expanding and cooling ever since. Later there gradually emerged the conditions necessary for the formation of atoms, still later the condensation of galaxies and stars, and about 10 billion years later the formation of planets. In our own solar system and on earth (formed about 4.5 billion years ago), the conditions have been favorable to the emergence of life. While there is little consensus among scientists about how the origin of this first microscopic life is to be explained, there is general agreement among them that the first organism dwelt on this planet about 3.5 - 4 billion years ago. Since it has been demonstrated that all living organisms on earth are genetically related, it is virtually certain that all living organisms have descended from this first organism. Converging evidence from many studies in the physical and biological sciences furnishes mounting support for some theory of evolution to account for the development and diversification of life on earth, while controversy continues over the pace and mechanisms of evolution. While the story of human origins is complex and subject to revision, physical anthropology and molecular biology combine to make a convincing case for the origin of the human species in Africa about 150,000 years ago in a humanoid population of common genetic lineage. However it is to be explained, the decisive factor in human origins was a continually increasing brain size, culminating in that of homo sapiens. With the development of the human brain, the nature and rate of evolution were permanently altered: with the introduction of the uniquely human factors of consciousness, intentionality, freedom and creativity, biological evolution was recast as social and cultural evolution.
In freely willing to create and conserve the universe, God wills to activate and to sustain in act all those secondary causes whose activity contributes to the unfolding of the natural order which he intends to produce. Through the activity of natural causes, God causes to arise those conditions required for the emergence and support of living organisms, and, furthermore, for their reproduction and differentiation. Although there is scientific debate about the degree of purposiveness or design operative and empirically observable in these developments, they have de facto favored the emergence and flourishing of life. Catholic theologians can see in such reasoning support for the affirmation entailed by faith in divine creation and divine providence. In the providential design of creation, the triune God intended not only to make a place for human beings in the universe but also, and ultimately, to make room for them in his own trinitarian life. Furthermore, operating as real, though secondary causes, human beings contribute to the reshaping and transformation of the universe.
A growing body of scientific critics of neo-Darwinism point to evidence of design (e.g., biological structures that exhibit specified complexity) that, in their view, cannot be explained in terms of a purely contingent process and that neo-Darwinians have ignored or misinterpreted. The nub of this currently lively disagreement involves scientific observation and generalization concerning whether the available data support inferences of design or chance, and cannot be settled by theology. But it is important to note that, according to the Catholic understanding of divine causality, true contingency in the created order is not incompatible with a purposeful divine providence. Divine causality and created causality radically differ in kind and not only in degree. Thus, even the outcome of a truly contingent natural process can nonetheless fall within God’s providential plan for creation." (paragraph 63, 68-69 from "Communion and Stewardship: Human Persons Created in the Image of God," plenary sessions held in Rome 2000-2002, published July 2004)
Pope Benedict XVI (Then Cardinal Ratzinger at the time when he made the following statement) stated that "We cannot say: creation or evolution, inasmuch as these two things respond to two different realities. The story of the dust of the earth and the breath of God, which we just heard, does not in fact explain how human persons come to be but rather what they are. It explains their inmost origin and casts light on the project that they are. And, vice versa, the theory of evolution seeks to understand and describe biological developments. But in so doing it cannot explain where the 'project' of human persons comes from, nor their inner origin, nor their particular nature. To that extent we are faced here with two complementary -- rather than mutually exclusive -- realities." (Cardinal Ratzinger, In the Beginning: A Catholic Understanding of the Story of Creation and the Fall [Eerdmans, 1986, 1995], see especially pages 41-58)
-Catholic teaching on creation-
In the Catechism of the Catholic Church on faith, evolution, and science in the 1997 edition are found in paragraphs 159, and 283-284.
159. Faith and science: "...methodical research in all branches of knowledge, provided it is carried out in a truly scientific manner and does not override moral laws, can never conflict with the faith, because the things of the world and the things of faith derive from the same God. The humble and persevering investigator of the secrets of nature is being led, as it were, by the hand of God in spite of himself, for it is God, the conserver of all things, who made them what they are." (Vatican II GS 36:1)
283. The question about the origins of the world and of man has been the object of many scientific studies which have splendidly enriched our knowledge of the age and dimensions of the cosmos, the development of life-forms and the appearance of man. These discoveries invite us to even greater admiration for the greatness of the Creator, prompting us to give him thanks for all his works and for the understanding and wisdom he gives to scholars and researchers....
284. The great interest accorded to these studies is strongly stimulated by a question of another order, which goes beyond the proper domain of the natural sciences. It is not only a question of knowing when and how the universe arose physically, or when man appeared, but rather of discovering the meaning of such an origin....
-Conclusion-
Today, Evolution and the Roman Catholic Church do not conflict with one another. Only faith and scientific finding regarding man's material body are not in conflict with the Church's teachings and that the existence of God is required to explain the spiritual component of man's origan. In short this sourt of view falls into the spetrum of the viewpoint of theistic evolution.