Bent three fingers back at mma practice. What kind of injury is that?

Sprain most likely. Most of the time when fingers are hyperextended back it causes a sprain (tear) of the ligaments. If it is a more severe injury you may have torn the tendon, causing an avulsion fracture where the tendon attachment to the bone is torn off. Be sure to ice your fingers, buddy tape them together. If you are having a hard time opening and closing your hand to make a fist go see your doctor.