An honorable mention is merely a name given to a distinction that may or may not be awarded at the end of a contest, exhibition, or competition. The definition of honorable mention implies that it is a distinction given to an entry worthy of mention, but not warranting top prize or first place.
An honorable mention can also be interpreted as a runner-up status in a contest. Contests that award prizes for certain placements may award an honorable mention or a runner-up distinction to its participants. The honorable mention could be simply the distinction or may include the same prize for all participants who earn that status at the end of the contest.
An honorable mention may be a better achievement in exhibitions than in prize contests. Literary and art competitions, for example, may award honorable mentions to their entrants who do not take first place, but the exposure that results from the distinction is often beneficial. Many competitions at least make note of an honorable mention or mentions in some fashion and while not first place, this can yield positive results such as public recognition, published recognition, or display and exhibition.