The difference is the scope of the object. A public object is accessible outside of the context in which it is declared - a private object is obviously the opposite, its not accessible outside the context in which it is declared. Basically if you want to access your function from another class call it public, if you only want it available within the class call it private.
Try reading an introductory book about .NET it will explain these concepts more completely and is easier to leverage than the help documentation if you are learning some general ideas.