As the comment says (in 2013b), it's to deal with callbacks (that getpts configured).
If you look further down (it's on line 74 in 2013b), getpts sets up callback methods that call getpts with a string. If you look even further down (line 177 onwards), you have functions with the same names as the strings in the callbacks. The whole thing is just to dispatch the callback to those functions.
The reason the callbacks are not set up to call these functions directly is because these functions are only visible from within getpts (since they're defined in that m file and are not the main function).
You could achieve the same thing with anonymous functions, which would have been cleaner, e.g:
set(fig, 'KeyPressFcn', @(o,e) privatefcn);