That phrase comes, of course, from the Declaration of Independence. It is the third of the unalienable rights, along with life and liberty. The word "property" often shows up as the third item on such lists, and does so for example in both the Bill of Rights and the 14th amendment. But Jefferson wrote of "life, liberty, and the pursuit of happiness."
Much heavy water has been made of this in the last 2 and 1/3 centuries. I'm reminded of an episode of The Sopranos in which Tony is complaining to his psychologist about his terrible life. He says that he saw a documentary on The History Channel in which the anchor said that the US is the only nation in the world with a founding document that explicitly mentions happiness.
"So where is my happiness," he cries.
Dr. Melfi, "'Pursuit' is what it says."
Tony: "Yeah, there's always a fucking loophole."
Anyway, one common question is the origin of Jefferson's phrasing. In the background stands John Locke as a critical figure in the education of the discontented colonists in general. But this wording in particular probably arose in response to more proximate suggestions.
Indeed, just a few days before the Declaration of Independence was issued, Virginia had published its own "Declaration of Rights," formally adopted on June 12, 1776. George Mason, the author of that document, had referenced "the enjoyment of life and liberty, with the means of acquiring and possessing property, and pursuing and obtaining happiness and safety."
Jefferson may have been thinking of Mason, and trying to achieve a more concise expression of the same idea. In that case, Jefferson's exclusion of "property" from his own wording doesn't imply any implicit demotion of it. It is there quite explicitly in Mason's wording, and Jefferson likely thought the connection between property and happiness too obvious to need another such explication.