When a mishap happens to someone's clothes, such as a bra snapping off. Usually accidental.

The term "Wardrobe Malfunction" became popular as a joke. During a Super Bowl Halftime Show ("Super Bowl XXXVIII" / Carolina Panthers VS New England Patriots) in which Janet Jackson and Justin Timberlake were doing a duet performance, towards the end Justin ripped away part of the bustier Janet was wearing, exposing her right breast. Her nipple was visible but her areola obscured by a gold star-shaped nipple shield.

The broadcast was live to the public, and there was no time to censor it. She later claimed that it was the result of a "Wardrobe malfunction", and thus the term was born.

(Copied from Danbooru)