Min Power is used when your laser is at or below what’s called the “start speed” - IE, the speed at which it starts ramping power up to the Max Power setting. By default, on Ruida, it’s 10mm/sec.
Glass tube lasers need a certain amount of power before they start ionizing and producing a beam. This is a higher value for larger tubes. Setting Min Power below this threshold means that when your laser starts moving, and is still using the “Min Power” setting, you get nothing. As it speeds up and ramps the power up toward the “Max Power” setting, the tube fires and you get output, but your corners won’t cut because the laser has to slow down for them, and as it does, and comes close to stopping, the power ramps back down to “Min Power” again, and if it’s too low the tube stops firing.