On July 4, 1776, the Continental Congress voted to accept the Declaration of Independence, the famous document that declared the American colonies to be independent from Great Britain. Almost a month later, on August 2, 1776, fifty-six members of Congress came forward to sign their names to a handwritten parchment copy of the Declaration. Most of these men held firmly to the content of the Declaration, all the way from its Preamble through its Declaration of Natural Rights and List of Grievances to the final Resolution of Independence.

The first of these four sections, the Preamble, sets forth the purpose of the document. It explains that sometimes it is necessary for one group to break its political ties with another group, especially when that latter group is violating the former's natural, God-given rights.

The second section, the Declaration of Natural Rights, proceeds to list those “unalienable Rights” in detail. God gives people the rights of “Life, Liberty and the pursuit of Happiness,” the document asserts, and government is meant to serve and protect those rights. When a government fails to do so (and in fact destroys such rights), especially after a long time and many attempts at reform, the people have a right to abolish such a dysfunctional government and start a new one. This is the position the American colonies are in, the Declaration proclaims.

The document then goes on to explain exactly why the colonies are in such a position in the Declaration's third section, the List of Grievances. The list is long indeed and covers legislative abuses, lack of representation, obstruction of laws and justice, the presence of standing armies, unfair taxes and control of the economy, and British aggression. The colonies have tried every means possible to petition for a fair redress of these grievances, but the king has shown himself a tyrant in every way, making him “unfit to be the ruler of a free people.”

Therefore, the Declaration concludes, the representatives of the new United States of America solemnly set forth a Resolution of Independence, declaring their states “Free and Independent” of Britain and assuming the power of war, peace, alliance, commerce, and all other acts of an independent country.

There are four parts to the Declaration of Independence:

The first section is the Preamble. In the Preamble section, the writers explain that if a group of people want to dissolve their government (as the colonists do), they need to tell the world why they want to do this.

The second section is the Declaration of Natural Rights, which lists the rights that all "men" have. These rights, called natural or unalienable rights, are rights that are granted by God and can't be taken away or given up. These include the right to life, liberty and the pursuit of happiness. The government has a responsibility to protect these rights, and when a government fails to do so, the people have the right to abolish that government and replace it with one that will protect these rights. The decision to abolish a government should not be taken lightly and should occur only after repeated violation of the people's rights.

The third section is the List of Grievances. This is the longest part of the Declaration of Independence, and it lists all of the complaints the colonists had about the British government and the King of England.

The fourth section is the Resolution of Independence, which states that the colonists have officially declared themselves free from the rule of the British government. It is in this section that the United States of America is officially announced. This section is followed by the signatures of the delegates of the Second Continental Congress.

Those are the four sections of the Declaration of Independence and what each section represents.

The Declaration of Independence does indeed have four parts.

The parts come in this order:

FIRST, the preamble basically says why the Continental Congress wrote the Declaration of Independence.  It states that when it becomes necessary because of injustice, a group of people should be able to state their grievances and take action.  The preamble is the first item in a document almost 100% of the time - thus, it is called the PREamble, or "explanatory stuff that comes first".  Other words for a document's preamble are "preface", like we have in books, or "introduction", like when a speaker is introduced before his speech.

SECOND, the Declaration of Natural Rights states that all human beings were given certain rights by their Creator and that the government should protect these rights.  

THIRD, the List of Grievances, gives a run-down of all the rights that the Continental Congress believed the British government, and King George III in particular, has violated.

FOURTH and last, the Resolution of Independence says what the Continental Congress has decided to do about all the aforementioned things.  In this section, the United States informs Britain that it has decided to become its own country.  

As you say, the Declaration of Independence has these 4 parts.

The first part is the declaration of natural rights. It says that people have these rights by the fact that they are human. These are not rights that the government gives them -- they have them automatically because they are people.

Then you have the preamble. It gives the reasons why the colonists think they have the right to rebel. It says that if their government doesn't protect their rights, they have the right to rebel.

The third section gives all the ways that (Jefferson claims) the king has failed to protect the colonists' rights. This ties in to the previous section and gives the specific things the king has allegedly done wrong.

Finally, the fourth section comes out and says "so now, because of this stuff, we are our own country."