There are many different varieties of social contract theory, but what all of them have in common is the notion that there is some kind of agreement between those who govern and those who are governed.

The type of social contract set out in the Declaration of Independence owes much to the political philosophy of John Locke. He argued that governments were set up to protect certain natural rights that the people enjoyed. By “people,” Locke meant men of property; indeed, he argued that the main reason for setting up institutions of government was to protect private property.

Locke further argued that if governments did not protect the people's natural rights and didn't fulfill their side of the social contract, then the people were entitled to change the government, by force if necessary.

This is precisely the same attitude set down in the Declaration of Independence. Many American colonists, including those who added their names to the Declaration, believed that the British colonial authorities had violated their inalienable rights. Under the circumstances, they were absolutely entitled to get rid of the present system of government and replace it with one that would protect life, liberty, and the pursuit of happiness.

The Declaration of Independence rejects the idea of the divine right of kings, which theorizes that since God appoints kings, they have the right to rule as they see fit. Under this concept of governance, if a monarch turns out to be a tyrant, he is an "iron rod" sent by God to punish the people for their sins. The worst crime, therefore, is rebelling against a king.

The authors of the Declaration of Independence repudiate that idea, basing their bid for independence on John Locke's Second Treatise of Government. In this work, Locke asserts that a monarch's legitimacy comes not from God above but from below, through the consent of the governed. Government is, in his mind, a contract between the governed and the monarch. If the monarch violates the rules of the contract, the people have the right to cast him out.

Locke defines the rules of the social contract in terms of Natural Law. People—at least white men—have certain natural and innate rights given to them by God which cannot be taken away. The Declaration of Independence sums up these rights as "life, liberty, and the pursuit of happiness." This document then goes on to outline in some detail the many ways George III has violated his side of the social contract. These violations, according to writers of the Declaration, justify the colonists in their bid to break away from British rule.

The above answer is incorrect in suggesting that people agree to give up some of their freedoms in order to have the government protect their truly important freedoms. This was the philosophy of Thomas Hobbes, who argued that unless this was done, life would be "nasty, brutish and short." Nowhere in the Declaration or in the philosophy upon which it is based, is it suggested that people must surrender ANY rights in order to secure others. In fact, Hobbes theory was used to justify the Divine Rights of Kings, which has no bearing in the Declaration--quite the contrary.

The Declaration was based almost entirely on Thomas Jefferson's understanding of John Locke's vision of the Social Contract as expressed in Locke's Second Treatise on Government. A comparison of the two is illustrative:

A.  Locke:  All men are  born with certain "natural rights." Among them are life, liberty and property.

Declaration:

We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness.

B. Locke: Pursuant to the Social Contract, governments are created for the sole purpose of protecting one's natural rights:

Declaration:

That to secure these rights, Governments are instituted among Men, deriving their just powers from the consent of the governed.

C.  Locke: People have the right to change their form of government if they believe it no longer protects their natural rights. Locke used this argument originally to justify the Glorious Revolution of 1688, in which James II was deposed and the throne offered to William and Mary.

Declaration:

That whenever any Form of Government becomes destructive of these ends, it is the Right of the People to alter or to abolish it, and to institute new Government, laying its foundation on such principles and organizing its powers in such form, as to them shall seem most likely to effect their Safety and Happiness.

 

The social contract is the idea that people get together and agree to give up some of their freedoms in order to have the government protect their truly important freedoms.  This idea is strongly reflected in the Declaration of Independence.  The Declaration says that governments derive their legitimacy from the consent of the governed.  This corresponds to the idea that people agree to be governed.  The Declaration also says that the government needs to protect people's rights to life, liberty, and the pursuit of happiness.  This corresponds to the idea that the government has to protect the people's important freedoms.  In this way, the Declaration very clearly upholds the idea of the social contract.