To be languorous is to be dreamy, lackadaisical, and languid. When someone is languorous, she’s lying around, daydreaming, possibly fanning herself lazily. It’s a little self-indulgent.
Languorous refers to a certain kind of mood everyone gets in sometimes — when you'd rather lie around thinking than doing work or having fun. When you're languorous, you're tired and maybe a little depressed. Things can be languorous, too — like a hot, languorous summer afternoon or a languorous song that’s slow and mournful. If you've ever lounged in bed for an hour after you were supposed to get up, you’re familiar with feeling languorous.