To do as one likes; to act as one wishes. Can also indicate permission or resignation toward someone else's actions, depending on context.
もう好きにしていいよ。私は関係ないから。
Do whatever you like. It's none of my business anymore.
部屋のレイアウトは好きにして構いませんよ。
You can arrange the room however you like.
彼は誰に何を言われても好きにするタイプだ。
He's the type who does as he pleases no matter what others say.