There's two sides to this.

Don't give a fuck about what those around you think but do give a fuck about the things that are important to you, the things that matter to you in life. Be passionate.

It's important to stipulate that otherwise people tend to have a habit of getting the wrong idea and mistaking "don't give a fuck" for "be a dick".

The point is basically to lose all the social fears and stop caring about any and all judgements others give you. When you do this you naturally act more confidently and more yourself, you stop living up to other's expectations and thus don't do any needy actions. At the same time you demonstrate that you you're passionate about the things that matter to you in life such as your friendships, your ambitions, your moral values, etc.

Don't care, but care.