Well first we have to understand what your subconcious is.

Basically it is the part of you that processes information all day long without you knowing. A good example i heard once was;

Ever tried to remember the name of a celebrity but just couldn't grasp it? Then you gave up and continued your day without thinking about it. Then later on it would just randomly pop into your head, "ah! Ozzy Osbourne!"

After you had given up thinking about it, your subconcious self went off into your 'memory banks' and found the answer.

I suppose lucid dreaming gives us access to our subconcious because we are in such a calm state that we ourselves can access our 'memory banks' instantly. We can also figure out if something has been troubling us that we have simply been ignoring or 'putting off' during the day. I guess thats why we have nightmares about things, our mind is saying "Hey you! Crazy faced-pace western society mug! Take a chill pill and sort out your issues eh?".