Alright, in Modern English, this means that the colonists were agreeing to form a government for the people, by the people, the first buds of democracy (before the House of Burgesses, anyway). The compact gave the settlers the power to frame and enact laws for the general good of the planned settlement.
The Mayflower Compact was signed in 1620 by Pilgrims, English people hoping to establish a settlement in North America. The agreement was completed on the ship Mayflower, which was anchored off the coast of Massachusetts.
Most of the Pilgrims were members of the Separatist congregation that had split from the Church of England. However, some were not, and these people sought independence from the Separatists. To prevent this, Separatist leaders wrote the compact, which was modeled after the covenant that had established their Separatist faith. Each male adult signed the document. The signers agreed to follow all "just and equal" laws that the settlers enacted and to be ruled by the will of the majority. Plymouth Colony did not receive an English royal charter, and so the compact determined governmental authority in the colony until it became part of the Massachusetts colony in 1691.