Without context, I'm going to make the assumption that this question arises from the new Sia song. Literally, "a bird set free," is "a bird (that has been) set free." Where "to be set free" means to be released." Metaphorically, the phrase means that you have been freed from some sort of burden or prison (emotionally, physically, etc.) If you are referring specifically to what the whole song means, then the sense that I get from the lyrics is that being held back, she fights to be heard and to do what makes her happy. When she finally breaks the "bonds" that hold her back, she is free. She may not be perfect, but she is doing what she loves.

It could mean anything -- Maybe Psalm 124:7.