It means to tell a person or animal to leave, either verbally or with hand motions.

Here are lyrics to a song which might help you understand the context. The original song is very racist. Shoo, fly, don't bother me, Shoo, fly, don't bother me, Shoo, fly, don't bother me, For I belong to somebody. I feel, I feel, I feel like a morning star, I feel, I feel, I feel like a morning star. Oh, shoo, fly, don't bother me, Shoo, fly, don't bother me, Shoo, fly, don't bother me, For I belong to somebody.