Well, the 18th-19th century is not my best period of history, but I will try:
Phanariotes were Greeks, from the city (or district? or region?) of Phanar. In the 18th and 19th centuries, there was the time when the Ottoman empire had most authority over Romanian lands. In 1600 for example, they didn't have the right to do or decide anything in Wallachia and Moldavia, just that those two countries had to pay a tribute. In the 18th century however, Wallachia and Moldavia were under Ottoman suzeranity, which means that the Sultan had little power if any over the people, and didn't have the right to govern the countries, but they had the right to decide who will be the ruler of the countries.
The Ottomans then used a new strategy when they had this power. They were selling the throne to whoever had most money to buy it from them. The Greeks in from Phanar were very rich merchants. The throne belonged to whoever had most money at a moment, this meaning that the Sultan gave the power to someone richer than the current ruler. This had a huge impact over the economy in Wallachia and Moldavia, because when one of those Phanariotes managed to become the ruler of Wallachia, they were stealing from the treasure of the state as much as they could, to make up for the money they paid to the Sultan. And if they got rich again, the same person could rule more than once (Constantin Mavrocordat reigned 4 times in one of the countries and 6 times in the other!)
This led to a period of poorness, dictatorship and foreign power over the 2 countries. Of course, some of the Phanariotes were good rulers, but those were so rare that they were not enough to make up for the huge number of bad rulers. They were merchants after all, they were not educated to rule a country.
The Phanariotes in Moldavia and Wallachia interacted a lot, many of them being alternatively rulers of Wallachia and Moldavia (again I bring up the example of Constantin Mavrocordat, who reigned 4 times in one of the countries and 6 times in the other. Since both Wallachia and Moldavia were about in the same situation, the Ottomans usually changed the ruler of one of them with the ruler of the other. All in all, there were a lot of people who didn't know anything about ruling a country and just wanted to get their treasures back after paying to the Ottomans.
