I guess it's something you say when you know you're going to eventually meet a person you say that to (because they live nearby or work at the same office), although you're not making any appointment with them this way. It's just a way of saying 'bye'.

The dependent the conversations Hey tomorrow is my birthday are you going to be there? Because I definitely want to see you around. Hey, I'm getting late from work so if you don't mind I will see you around then. I haven't seen you for a long time. When did you came back to town? Anyways it's good to see you around.

"I'll see you around" means "between or within" I'll see you around 5 O'clock today, I'll see you within 2hours