Pax Americana: "Historical concept of relative peace in the Western Hemisphere and later the Western world resulting from the preponderance of power enjoyed by the United States". (Wikipedia)
Sounds about right to me. Compared with Pax Romana ("long period of relative peace and minimal expansion by military force experienced by the Roman Empire in the 1st and 2nd centuries AD") and Pax Britannica ("period of relative peace in Europe and the world (1815–1914) during which the British Empire controlled most of the key maritime trade routes and enjoyed unchallenged sea power") it fits rather well.
All it describes is that the nations and territories under the control or influence of the United States experienced a peaceful time. Which is true.
[For dramatical reasons, I'll replace the USA with the Empire in the rest of the post.]
The areas where conflict did happen were places where the Empire did not have control, and thus sometimes got into conflicts with the local interests, or even groups supported by the Evil Empire, the Other Evil Empire and others. The nuclear deterrent probably was a big reason why no full-scale war ever developed between the super-blocks.
Within the Pax Americana, life has been relatively peaceful. True, dictators was allowed to run around freely as long as they never hurt any of the Empire's interests. And true, vassalised smaller Empires and others have fought wars or been involved in conflicts, but never against another nation within the Pax (I can't think of any right now at least).
However, countries who weren't treated as nicely by the Empire, or countries along the border of Pax Americana, could often be economically disadvantaged, as they were forced/pressured into adopting policies which benefited the Empire more than themselves. Countries that didn't comply, or which gave the Empire reason to suspect they were planning to support the Evil Empire, suffered invasions or coups committed or facilitated by the Empire.
- Chile was one of the countries which tried to go their own way, and was subdued by a military coup.
- When Argentina took control of the Falklands, it is doubtful that the British would have retaken the islands without moral support/permission from the Empire. As the Empire feared that Argentina would form closer bonds with the Evil Empire when their negotiations didn't lead anywhere, they let the British retake the islands and supported them in doing so. Chile, which now was fully serving the Empire, provided intelligence, and France and other members of Pax Americana provided support and helped isolate Argentina.
- Libya was run by a dictator who preferred to be his own master. He managed for quite a while, with a mix of providing cheap oil to Europe and buddying up with both superpowers. His hostile acts put him in a dangerous position however, and it was only after the Evil Empire was gone and he started to repent that he was taken back into the fold (Where he was treated as a friend and part of Pax Americana until the Arab Spring).
- Iraq also tried to play the big game, but when they invaded Kuwait they became too powerful for the Empire's taste. Iraq was beaten, isolated and suppressed, until it was finally conquered and the leaders executed when the Empire had lost all its patience.
- Syria is currently in a civil war, and that has been "allowed" to continue because they aren't a part of Pax Americana. With the help of the Evil Empire and later Russia, they've survived outside the control of the Empire. At the moment, the Empire doesn't feel a strong obligation to help a country which isn't part of its domain, and in any event, it is not strong enough to do anything because Russia also has a great amount of influence, and a different agenda.
[I'll stop the dramaturgy now before Dachs or anyone else beats me up for writing false/inaccurate history, but you get the point.]
In many ways I think it is possible to see a Pax Americana in the politics and history of the last ~70 years. Thinking of the USA as the empire, in the same way as Rome or Britain used to be, isn't completely unreasonable.
So if Pax Americana existed, does it still exist, and was it a good or bad thing?
I'd say it existed and had it's greatest power after the Cold War and until around these times. It still exists, but now other nations outside the control of the USA are now growing economically. Soon they will use this economic power to empower themselves militarily and politically, which means that Pax Americana will not be as powerful as it used to be.
Pax Americana has primarily served the rulers of the USA of course. The American people have, by proxy, also enjoyed many benefits from it, and the same is true for the people in Western European countries and other places that enjoyed the sympathies of American realpolitik. For others, not so much.