As a Fetish
Damsel in distress is a type of fetish that revolves around a heroine in trouble, usually tied up in a form of bondage by the enemy. There are also damsel-works of characters being held prisoner in a jail cell while tied up included in this clique.
For Japanese, the abbreviation "DID" is often used to describe damsel-in-distress in their dialogue, as well as tagging illustrations on pixiv.
Generally speaking, the term refers to any character struggling to release themselves from their restraints, regardless of the situation.
There is also a male of damsel in distress, under the abbreviated tag GID (Guys in distress), although it is less known about it. However, it's also an innocuous abbreviation for gender identity disorder, which share the same abbreviation.
As a Trope
A damsel in distress is where a character (particularly female) is held in captivity by an evil do-er and it's up to the hero of the story to save them. Love, heroism, and motivation are common emotional setters during the story.
The damsel in distress trope was popularized back in the 80-90s within several media. The Super Mario Bros. series was a notable example, famously features Mario rescuing Princess Peach from his nemesis Bowser.
However, in later years, the trope has stagnated and became a topic regarding the stereotypical depiction of women in fictional media. Within time, the damsel-trope became a disused device and nearly forgotten over time.
Related tags
Restraint Bondage Kidnapping Cage