Endermen are tall, lanky, black creatures that primarily inhabit the End. The End is known to have some space distorting effects as it is a part of another dimension. This explains why Endermen can teleport, but what exactly are they?

It is most likely that the Endermen are the last living remnants of the ancient race of builders. Based on what we know about the Nether, we know the builders were either exploring beyond their capacity or trying to escape something. Their exploration led them to The End where they set up settlements. Long-term exposure to the strange dimension changed the builders into Endermen.