Damsels are blonde women in red dresses who can be picked up and carried in the same manner as a corpse.
They can be found randomly generated in the dungeon or in certain shops. Damsels in shops are treated as property of the shop, and you will be treated as a thief if they leave it (whether being carried out or running away on their own after being picked up).
The main purpose of a Damsel is to give the Spelunker more health at the end of the level. However, they do have some other uses as well: They can be sacrificed at an altar for a large amount of favor, used as a makeshift throwing weapon (or suicide bomber), or to soak up damage from traps and other projectiles. Damsels can also be used to stun mantraps, although this will usually kill the damsel.
Throwing or dropping them will result in their being stunned for several seconds. A Damsel who has been picked up and dropped or thrown will eventually come to her senses and begin running around panicking. The Damsel will run in one direction, will fall off platforms (making her fodder for spike traps and (Wo)mantraps) and will only turn if she hits a wall.
They have four hitpoints of health, but do not take fall damage, whip damage, or damage from enemies other than mantraps. Bringing them to a level exit will cause them to kiss you and give you an extra heart when you leave.
Dead Damsels can still be carried and thrown at enemies. However, you get no reward for carrying her corpse to the end of the level, so you may as well sacrifice her body if you find an altar.
As a Playable Character
The Damsel is also a playable character and can be unlocked by opening the Changing Room. She has all the same abilities as the Spelunker.
When the Damsel is the player character, Spelunkers spawn randomly in the levels instead and can be saved for kisses or sacrificed for favor like the Damsels usually are. While playing as a Damsel, she will always appear to be panicking as she runs as she has no 'ordinary' walking animation.