The Declaration of Independence formally announced the independence of the colonies and their breaking away from Great Britain. They wanted to be able to explain why they wanted freedom, revolution, and how they were a new country.
The colonists wanted to be independent mainly because they felt as if Great Britain was treating them unfairly. Before the French and Indian War, Great Britain had practiced salutary neglect with the colonists. There was no problem, as the colonists were mainly left alone and were not being interfered with. After the French and Indian War, Great Britain had stopped practicing salutary neglect in order to pay for the very expensive war.
This meant that Great Britain started taxing the colonists, which they despised and felt it was completely unfair because they had nobody to represent them in the British Parliament, known as "taxation without representation." Great Britain defended themselves, however, saying that they needed money to pay for the French and Indian War, which was fought on their soil. They also stated that they were using their troops in order to protect the colonists from Native Americans, so their taxing was justified.
Along with taxing, the colonists also did not like other things that Great Britain did, like the Quartering Act and the Intolerable Acts. They felt as if Great Britain was overbearing and unfair and simply wanted independence from them.