This phrase is very informal and best used among friends or in casual conversations, not in formal situations. She doesn't give a stuff about following the latest fashion trends.
Pro Tip 2/3
Emotional Detachment
The phrase often implies a strong indifference that suggests the person is emotionally detached or uninterested. He didn't give a stuff when he heard they lost the game.
Pro Tip 3/3
British Origin
Originally British slang, this phrase may be less understood or used in other English-speaking cultures. When I visited the US, it seemed they didn't give a stuff about cricket.