Photographers seems to love to say this. Is this still considered funny?
Because of the way that Cheese should be pronounced, especially when it should be pronounced emphatically (the exclamation mark at the end), it should cause your cheeks to rise and your lips to part and your eyes to slightly lower on the corners. This causes your face to lighten.
Additionally, it is rather an odd command, so it generally induces people to smile while opening their cheeks and exposing more of their face to the camera.
But really, just smile wide and look at the camera (and don't blink!)
The idea behind "say cheese" is not to make a joke, but to get your mouth into a position that resembles a smile. Depending on how you say them, ee sounds like in cheese can cause you to widen your mouth, sort of like a smile.
(Of course, unless you're being a wise-ass, you shouldn't actually say cheese, or anything else really, when you're told to "say cheese"; instead, you should just smile to the best of your ability.)