Paralyzed
A paralyzed creature is incapacitated. While paralyzed, the creature cannot move, but typically stays standing.
Attacks against the paralyzed creature have advantage.
Any attack that hits a paralyzed creature that is either a melee attack or made from within 5 ft. is a critical hit.
Notes
Regarding ranged attacks made against paralyzed and unconscious creatures:
A ranged attack made from 30 ft. away against a paralyzed target has advantage.
A ranged attack made from 30 ft. away against an unconscious target has advantage and disadvantage (because the unconscious creature is prone). In this case, the attack is rolled without advantage or disadvantage.
A ranged attack made from within 5 ft. against a paralyzed or unconscious creature has advantage and disadvantage. The attack is rolled without advantage or disadvantage. Such a ranged attack becomes a critical hit as long as it hits.