Very simply put, a lucid dream is a dream in which you are aware that you are dreaming. So long as you remain conscious of this fact you remain lucid (‘lucid’ is synonomous with ‘aware’ or ‘clarity’.) Lucidity is a sense or more a ‘knowing’ of your participation in dream reality, brought about by the realization that you’re dreaming.
The degree of your lucidity will vary between lucid dreams. You may be dimly aware that this is a dream, you may be consciously participating in a ‘normal dream’, you may have partial recognition and control, or you may be fully aware and awake inside your own dream world. This last is what most lucid dreamers aim for.
You’re likely to experience each of these in stages as you learn lucid dreaming, and each experience is a kind of breakthrough into greater awareness. As you increase this dreaming awareness, the more fully lucid dreams happen more regularly. For this reason lucid dreaming does get easier every time, just as with any practice you can get good at.
Lucid Dreaming implies a certain degree of dream control, though this also develops over time. Mostly because it takes a while for it to sink into your conscious awareness in a usable way that you can do anything, that you actually are control. But once you ‘get’ that, the possibilities are limitless!