Brief Summary
The Set-Up
By the time the Declaration of Independence is penned, the English colonies in North America have been around for a whopping hundred and fifty years. And then England starts doing a bunch of not-so-nice things, and passing a bunch of laws that take advantage of the colonies without granting them representation in Parliament.
For obvious reasons, the colonists are none too pleased, and they eventually decide enough is enough, declaring themselves an independent nation. (Woo-hoo! 'Murica!)
The Text
The purpose of the Declaration of Independence isn't just to say that the colonies are now independent from Britain, but also to rationally explain why such a separation is necessary. (The "rational" part is uber-important: they can't just say "Because Britain sucks.")
First, Jefferson first discusses the inherent rights of human beings, and how government is meant to protect those rights. Next up? He launches into a more specific list of abuses that the English government has inflicted on the colonies, which demonstrate how those human rights have been violated. Oh, and he also mentions that time when the colonists tried to get the British people on their side, and got no response. You know, just to reiterate why they needed total independence from the mother country.
The text contains big ideas about the role of government in relation to the people, as well as historical reasons why the colonies need to be independent. Jefferson and the other Founding Fathers are looking for government created by the people for the purpose of their protection, which is what they say will be implemented in their new country.
In other words, go away King George; we don't want you in our club anymore. You're breaking way too many of the rules and it is not cool.
TL;DR
King George III had been doing some shady things in his American colonies, and the colonists get super peeved, so they send him a very strongly worded letter saying they're starting a shiny new club across the pond…and he's not welcome.