The Mayflower Compact was an agreement signed by 41 of the Pilgrim men on the Mayflower. The men and the other Pilgrims were travelling to America to set up a colony that they could run according to their religious beliefs. The men signed the compact, agreeing to set up a government in their colony and agreeing to obey that government. This is seen as the first written constitution in American history.
We can argue that the Mayflower Compact is not really relevant today because it does not impact our everyday lives. We are not governed by the Mayflower Compact and it has no status as a legal document anymore. However, it is also possible to say that it remains relevant. If it does, it is because it was the first document that set out some of the fundamental things that we believe in.
For example, this was the first document from what is now the United States to say that government existed because the people agreed to it. This idea was taken up by Thomas Jefferson and put in the Declaration of Independence. It was the first document to say that laws should be created that are just and equal. It was, perhaps most importantly, the first time that we see the idea that Americans should have a constitution that specified (if only very generally) how they are to be governed. This document (arguably) remains relevant today because it is the first statement of some of the most important ideas of American government.