Bell's Palsy results from inflammation of the facial nerve (7th cranial nerve), which innervates the muscles of the face. It is not, however, responsible for feeling in your skin; this is done by the 5th cranial nerve.
The result of this is that muscles on the affected side of the face go limp, and you look like someone suffering from a stroke.
This inflammation is often caused by a viral infection and is treated with antiinflammatories until the infection is gone. Bell's Palsy is only temporary the majority of the time, but it can result in long lasting effects. I once dated a girl who suffered from Bell's Plasy a few years earlier, and she still had very minor symptoms of it in some muscles around the eye. There were not easily visible unless you looked for them, though.