Not "nature" as in "let's go look at the pretty birds in the pretty trees," which sadly doesn't appear in the Declaration of Independence, but rather the idea of what inherently exists in the world.

In the very first sentence, Jefferson discusses "the separate and equal station to which the Laws of Nature and of Nature's God entitle them," (1) in reference to people who declare independence. There's also that famous phrase, "endowed by their Creator with certain unalienable Rights" (2). Obviously there is a religious theme here too, but in the 18th century the two ideas are connected.

Jefferson argues, as others did around this time, that people are born with certain rights by virtue of being human beings. Those rights, given by nature (in the broader sense of the word) instead of man, are the reason why oppressive governments should be overthrown.

Jefferson calls upon a force greater than mankind, which can't be argued with or disputed, as proof of the colonists' legitimacy. It's not like Parliament could fight against the natural order of the world, unless they unlocked a magical secret that they have kept out of the history books over the centuries. (If we ever find out that's true, we'll have to re-read Harry Potter in a very different light.)

The focus on man's natural rights is therefore hugely significant for the Declaration. It provides a potentially ironclad justification for the colonies' freedom. It also brings up a larger philosophy, going against centuries of hierarchical society, to claim that people are born equals, because that is how nature creates us.

This idea, so fundamental in the founding of the United States, became part of the character of the brand new nation, and has been ingrained ever since as part of the vision of America. It's the "land of opportunity" because all are equal here…in theory.