It varies by school, but it is usually the offering of a set of perks to the top-end entering students at the school. Such perks may include priority access to smaller honors courses and seminars, priority registration in general, honors dorms, etc… The intent is to attract students who (while in high school) have the kind of elitist feeling that the big not-as-selective school does not have enough top-end students like themselves, or that such top-end students may be hard to find among the masses.
Here is a web site about honors programs at public universities: http://publicuniversityhonors.com/