This phrase is found in the opening passage of the Declaration, where Jefferson is explaining why a declaration is needed in the first place. In this context "station" means something like "status" or "position." So Jefferson is saying that sometimes countries and peoples have to leave, or declare independence from their mother country in order to gain the free and equal status they are entitled to by "the laws of Nature and of Nature's God."
This is the purpose of the Declaration, and the justification for it. It goes on to claim that being under British control has denied the colonists their natural rights, and that only by leaving the British can they set up a government that will protect these rights. This was a serious decision to make, and they thought a declaration that gave their reasons for making it was necessary. They were ready, they proclaimed, to claim an equal "station" among the other independent nations of the world, but this nation would be different, they said. This government would be based on the will of the people.