What does hypnotic mean?

I suffer from insomnia. I was on Ambien and now I’m on Lunesta, both of which are hypnotic medications. What is a hypnotic medication? Does it hypnotize me?

It just means sleep-inducing. Greek “hypnos” = sleep.

If I am hypnotized, am I asleep?

Well, no. The term “hypnosis”, meaning inducing a trance as a therapeutic method (or in order to make you quack like a duck, or whatever) is a bit of a misnomer. The term was coined by physician James Braid in 1842, based on the technique known as mesmerism, after Franz Anton Mesmer (who used the term “animal magnetism”). Braid believed the state was a form of sleep, but later he changed his mind and tried to change the name to “monoideism”, meaning “one word” or “one thought” (the idea being that the subject is focusing on one thing to the exclusion of all other thoughts, which induces the trance). However, the name “hypnotism” had already stuck.

(The whole history of the thing, though, is of course a lot more complicated. Some Wiki links.)

However, in the context of the OP, the term "hypnotic ", as I said, just means sleep-inducing, and has nothing whatsoever to do with hypnosis in the other sense.