Jefferson's main goal in writing the Declaration of Independence is well stated in the introductory paragraph of the document when he writes it is necessary to "declare the causes which impel them [the United States] to the separation." Jefferson masterfully paints a picture of abuse which was without doubt intended to make his readers feel sympathetic to the plight of the colonists.
His next move is to show the virtue of the Americans, that in the face of such abuse, they still clung to the hope of diplomacy in the spirit of forgiveness. In spite of that, their overtures of peace were "answered only by repeated injury." Again, this would serve to cause both sympathy and anger in the reader as the British are vilified in brutalizing someone bearing a banner of peace.
Jefferson's strongest appeal is to the faith of his readers by stating that "they [were] endowed by their Creator with certain unalienable Rights..." and that it was the job of the government to protect them. In addition he pointed out "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." Jefferson effectively portrays the Americans as carrying out the will of God in opposition to the tyranny of the British. This would certainly have resonated with his contemporaries to rally them around the cause of revolution.