It's a polite way to make a request or ask for something. You can use it in a variety of situations, just like you would use "please" in English.
Here are some examples:
* Bonvolu fermi la pordon. (Please close the door.)
* Bonvolu doni al mi glason da akvo. (Please give me a glass of water.)
* Bonvolu paroli pli laŭte. (Please speak louder.)