The Mayflower Compact is a very short agreement that was written up and signed by the Separatists (better known as the Pilgrims) on the Mayflower before they disembarked in Massachusetts. The ship was supposed to go to Virginia, but went off course. This led to some disagreement as to whether there would be any legitimate government in the colony (since they were not in the place where their charter from the king said they would be). To prevent this from becoming a problem, they wrote the Compact.
The Compact is significant in US history because it is seen as the start of democracy in America. This is because the Compact is a document in which the signers willingly give their consent to be governed by a government that they would set up themselves. Thus, the Compact is sort of like a first democratic constitution for an American colony.