You called lsqnonlin. One or more times while lsqnonlin is running, it calls the function handle with some input arguments it has computed. Calling that function handle calls bspline_registration_image with the input lsqnonlin computed as well as the inputs sizes, Spacing, I1s, I2s, and type you specified when you constructed the function handle.
Think of a function handle as a way to refer to a function that doesn't require hard-coding the name of the function. Using function handles gives you the flexibility to call lsqnonlin and have it call bspline_registration_image one time and Neda_custom_registration_image the next, without requiring any changes to lsqnonlin itself.
