A Rare Phenomenon is the third part of a series of Achievements. Each of the three requires players to kill a certain number of the Rare enemies that are on the list. Keep playing Diablo III, and you will eventually earn all three of these Achievements.
Rare monsters are yellow and are tougher to kill than the blue Champion monsters. They always have minions linked to them (which are harder to kill then the regular versions of those type of monsters).