For a GCode controller it’s only used to set the low-power value when grayscale engraving.
DSP controller do that too, and use it as the power value used when cutting at or below the “Start speed” setting in your controller. As you ramp up above the start speed to your chosen cutting speed, the power is ramped from min to max. If you’re doing slow cutting, or vector scanning, you’d generally just set them the same. It’s most useful when vector marking or cutting thin material to make sure you don’t overpower the corners.
For diode systems, you’ll want to set Min to 0 (or very slightly above) and Max to 100, and then vary the speed until you get a good result. Typically for a 2.5w diode would be in the neighborhood of 3000 to 4500 mm/min (50 to 75 mm/sec).