The Mayflower Compact is an important document for the reasons cited by the previous posters, but we should see this document in its historical context. Its most truly important point was that it was actually written down and then signed by every adult male, thus affirming that they had agreed to it voluntarily, not because of any existing legal or political issue or pressure. It is the first document of its kind in North America, but it is based firmly on the central contexts of British law, and was not seen by the authors as any kind of revolutionary statement. It did, however, firmly set the principle of equality among all citizens (or at least adult male citizens), simply because they all signed it. The document actually says nothing about what laws they would live under, or majority rule, or anything else of the kind. The document reads:
"IN THE name of God, Amen.
We whose names are underwritten, the loyal subjects of our dread sovereign Lord, King James, by the grace of God, of Great Britain, France and Ireland king, defender of the faith, etc., having undertaken, for the glory of God, and advancement of the Christian faith, and honor of our king and country, a voyage to plant the first colony in the Northern parts of Virginia, do by these presents solemnly and mutually in the presence of God, and one of another, covenant and combine ourselves together into a civil body politic, for our better ordering and preservation and furtherance of the ends aforesaid; and by virtue hereof to enact, constitute, and frame such just and equal laws, ordinances, acts, constitutions, and offices, from time to time, as shall be thought most meet and convenient for the general good of the colony, unto which we promise all due submission and obedience.
In witness whereof we have hereunder subscribed our names at Cape-Cod the 11 of November, in the year of the reign of our sovereign lord, King James, of England, France, and Ireland the eighteenth, and of Scotland the fifty-fourth. Anno Domine 1620."
The type of local government the Pilgrims had in mind already existed de facto and de jure in Virginia since 1607, so Massachusetts was not the first colony to opt for a democratic style of government in the New World. Nor would the Compact infringe on the British Crown's rights under the charter the colonists brought with them from England, which unfortunately for Massachusetts included the right to revoke the charter later. And although we were probably all told in school that the Compact includes the power of majority rule, in actuality the Pilgrims lived under the general ideals of the Puritans. Puritans did not believe in the rule of the majority. Community decisions had to be reached by concensus, which meant that all issues had to be thrashed out until a decision was reached that everyone could live with. Of course, this did mean that sometimes people were forced to leave the colony voluntarily or were exiled if they could not bring themselves to put up with the group concensus, and that sometimes the concensus was essentially "we agree to disagree", but majority rule was officially frowned upon by the government of Massachusetts colony until well past the time of the Salem and Andover trials, in other words until the beginning of the 18th century.
So to summarize, the Compact made plain the equality of all in the group who could vote; their agreement to govern themselves; and the group itself as the source of political power locally, under the authority of the King.