As you probably know, Botox is short for "botulinum toxin". This refers to the toxin (botulin) secreted by a particular bacterium - Clostridium botulinum.
The toxin has a particularly interesting, if devastating effect: it blocks the release of acetylcholine from nerve endings. Acetylcholine is common neurotransmitter, in this case used by the nerves supplying skeletal (voluntary) muscle as a signal to make them contract. In the absence of its release therefore, the muscle does not contract. In botulinism, the real problem comes when essential muscles stop working, particularly the diaphragm - the patient can die of respiratory failure.
Acetylcholine is also used as a neurotransmitter by other nerves, like those in the parasympathetic nervous system. Thus humans contracting botulinism typically display symptoms of both unopposed sympathetic activity (due to the suppression of the parasympathetic supply) as well as, more noticably, muscle weakness (e.g. difficulty swallowing, slurred speech, respiratory failure).
Sounds nasty, and it is. But in absolutely tiny doses, it has recently been used in cosmetics to relax the muscles causing the tiny skin folds of wrinkles. Go figure.
Other medical uses include relieving the muscle spasticity of conditions such as cerebral palsy and strokes, as well as achalasia (a condition where the lower oesophagus is chronically in spasm).