Clearly, from the comments, everyone's honors program is different. I think you should look carefully at the requirements at your school and decide if you are interested, though I think the opinion of adcoms should have NO weight in your decision. College is about more than preparing for med school. It's an important experience in and of itself.
I was in the honors program at my college. I applied before I ever decided to become a Dr. I just figured if I had to go there (b/c of financial aid issues) as opposed to more competitive schools that I had gotten into, I might as well do the honors program. The program has changed several times since I was first admitted, but basically, it entailed a half tuition scholarship, and certain requirements for each year: honors freshman english, an interdisciplinary honors course sophomore year, an honors project junior year, a senior honors seminar, and the option of an honors thesis. The major perks: the scholarship obviously, weekly honors teas w/good food and guest speakers, each honors class had a budget for cultural events in the city, New York Times subscriptions, and last year, they added an honors scholarship for studying abroad that only honors program students could apply for. Also, only honors students could take interdisciplinary classes, which were always cool. Stuff like Islam and the West, the Math of Art, Origins of Conscience through biology and philosophy, etc. I took Origins of Conscience and it was one of the best classes I ever took. Mostly, I liked the Honors Program b/c it allowed me to take classes that challenged me, and I like a challenge.