If something is sleepless, it's wakeful or restless, like a sleepless night spent in an unfamiliar house listening to spooky noises.
You might be sleepless the night before an exciting trip, or sleepless in your sleeping bag because the ground feels cold and hard beneath you. Whenever sleep won't come—because of worry, excitement, or discomfort—you can describe yourself (and the night) as sleepless. It's used in a literary way as well, to mean "restless" or "constantly moving," like a sleepless willow tree swaying in the breeze.