Unfortunately, Thomas Jefferson himself never explained his use of the phrase "pursuit of happiness" in the Declaration of Independence. However, he was almost certainly influenced by George Mason's Virginia Declaration of Rights (adopted June 12, 1776), which referred to "the enjoyment of life and liberty, with the means of acquiring and possessing property, and pursuing and obtaining happiness and safety" (Section 1).1
Jefferson's rough draft of the Declaration used the expression, "...life, & liberty, & the pursuit of happiness;" and in the final version of the Declaration it was altered slightly to "...Life, Liberty and the pursuit of Happiness."
Ellis, Joseph J. "The Spring of '76: Texts and Contexts." In What Did the Declaration Declare?, edited by Joseph J. Ellis, 79-94. Boston: Bedford/St. Martin's, 1999. See especially pp. 88-90.
1. The full text of the Virginia Declaration of Rights, along with draft versions and other related documents, is available online at the Gunston Hall (Home of George Mason) website: http://gunstonhall.org/documents/vdr.html.