A strong overall theme of the Declaration of Independence is that people are born with natural rights. Perhaps the most memorable phrase from the Declaration is the one you quoted, which uses the term "unalienable rights" as an equivalent for natural rights. Because the rights belong to us by nature, we cannot be separated or alienated from those rights.
Thomas Jefferson (writer of the Declaration of Independence) and other American founding fathers got their ideas about natural rights from philosophers of the Enlightenment, such as John Locke (1632-1704). Locke strongly argued that all human beings have certain natural rights which are to be protected and preserved. Locke's ideal was one that promoted individual freedom and equal rights and opportunity for all. Each individual's well-being (life, health, liberty, possessions) should be served by the way government and society are arranged. The American founding fathers accepted the views of Locke and other Enlightenment thinkers and acted on them.
John Locke, in his Second Treatise on Civil Government (1690), expressed these ideas as follows. Notice similarities to what is said in the Declaration of Independence (1776) ...
- The state of nature has a law of nature to govern it, which obliges every one: and reason, which is that law, teaches all mankind, who will but consult it, that being all equal and independent, no one ought to harm another in his life, health, liberty, or possessions… (and) when his own preservation comes not in competition, ought he, as much as he can, to preserve the rest of mankind, and may not, unless it be to do justice on an offender, take away, or impair the life, or what tends to the preservation of the life, the liberty, health, limb, or goods of another.