In modern language…
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, &c. Having undertaken for the Glory of God, and Advancement of the Christian Faith, and the Honour 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 another, covenant and combine ourselves together into a civil Body Politick, for our better Ordering and Preservation, and Furtherance of the Ends aforesaid: And by Virtue hereof do enact, constitute, and frame, such just and equal Laws, Ordinances, Acts, Constitutions, and Officers, 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 hereunto subscribed our names at Cape-Cod the eleventh of November, in the Reign of our Sovereign Lord King James, of England, France, and Ireland, the eighteenth, and of Scotland the fifty-fourth, Anno Domini; 1620.
Before making their journey to the New World, the Pilgrims had lived for some years in Leiden, a city in the Dutch Republic. Historian Nathaniel Philbrick notes, “Just as a spiritual covenant had marked the beginning of their congregation in Leiden, a civil covenant would provide the basis for a secular government in America.” — Wikipedia
The Pilgrims understood the need to create a secular form of government. One that adhered to their religious principles, but was not in itself religious. They also made clear that their allegiance was still to the king.
Plymouth Colony – Wikipedia
Mayflower Compact | North America  | Britannica.com
Rough seas and storms prevented the Mayflower from reaching its intended destination in the area of the Hudson River, and the ship was steered instead toward Cape Cod. Because of the change of course, the passengers were no longer within the jurisdiction of the charter granted to them in England by the Virginia Company. Within this legally uncertain situation, friction arose between the English Separatists (the Pilgrims) and the rest of the travelers, with some of the latter threatening to leave the group and settle on their own.
To quell the conflict and preserve unity, Pilgrim leaders (among them William Bradford and William Brewster) drafted the Mayflower Compact before going ashore. The brief document (about 200 words) bound its signers into a body politic for the purpose of forming a government and pledged them to abide by any laws and regulations that would later be established “for the general good of the colony.” The compact was signed by nearly all of the Mayflower’s adult male passengers (41 of a total of 102 passengers) while the ship was anchored at Provincetown harbour. Its authority was immediately exercised when John Carver, who had helped organize the expedition, was chosen as governor of the new colony.
The Mayflower Compact was not a constitution but rather an adaptation of a Puritan church covenant to a civil situation. Furthermore, as a provisional instrument adopted solely by the colonists, the document did not solve the matter of their questionable legal rights to the land they settled. (A patent was eventually obtained from the Council for New England in June 1621.) Still, the Mayflower Compact became the foundation of Plymouth’s government and remained in force until the colony was absorbed into the Massachusetts Bay Colony in 1691. Although in practice much of the power in Plymouth was guarded by the Pilgrim founders, the compact, with its fundamental principles of self-government and common consent, has been interpreted as an important step in the evolution of democratic government in America.
— Encyclopaedia Britannica