To emphasize their easygoing and carefree personality a person is wearing their shirt or jacket completely unbuttoned/unzipped.
It doesn't have to be permanent. An otherwise modestly clad character may temporarily adopt this image to indicate, that they're on their "off time".
This trope is not necessarily limited to male character nor is it required they don't wear anything else underneath.
Examples:
Anime and Manga- Franky of One Piece is a boisterous cyborg guy wearing his shirt unbuttoned 24/7.
- Zeebarf's Reemus is the type of guy who prefers if his trouble took care of themselves. One of them being buttoning his vest.
