Hey,
I am not sure what MU, MT, or MR means, but the 71H is the load index and speed rating. The 71 is the load index which when you look the load index up it will let you know the max weight that tire can hold and certain psi amounts. The "H" is the speed/performance rating which lets you know what speeds that tire can travel without the tire heating up and busting. Sports bikes most likely have a "Z" rated wite which can withstand speed of 149mph+. The "H" rated can go up to speeds of 130mph.
On cars now days there are S, T, H, V, Z speed/performance ratings(There are others, but those are the basic). The lower the rating the harder the rubber and it gets softer as it goes up. The softer rubber tires give better handling and cornering(provided the car calls for it), but softer rubber tires also suffer from less mileage wear. I hope this helps some.