Well, there are lots of ideas in the Declaration, but the main idea is that the people of the 13 colonies (not yet the United States of America) were tired of not being treated equally as British citizens.
They were unfairly taxed and had no representation in Parliament ("for imposing taxes on us without our consent").
Many of the specific ideas of the Declaration are jabs at the king, letting the world know why they felt the need to separate from the British thrown (for instance, "He has kept among us, in times of peace, standing armies without the consent of our legislature").
Many of the amendments in the Bill of Rights are based on things that the king of England did to the colonists.