Paralysis is a magically-induced inability to move, caused by floating eyes, gelatinous cubes, shades and potions of paralysis. It can also be caused by Magicbane hitting you, as opposed to hitting a monster. As with other forms of immobility, it wears off after a specific number of turns (as opposed to moves).
Wearing a ring of free action protects against paralysis.
Monsters can also be paralyzed, e. g. non-reflecting pets fighting a floating eye. You can wake them up with nonmagical or uncharged drums or horns.