Dana Sorensen and Jono Green, co-owners at Symbiotic Training Center, talk about stability(both upper and lower body) in throwers, like pitchers in softball.
Good stability means a player's ability to keep their joints mobile while also protected in their correct range of motion. Many joints can only function one at a time, meaning that one joint must be stopped so that another joint can function.
Mobility training and stability training can include strength exercises, range of motion exercises (such as band work for shoulders) and speed/acceleration training (such as sprints from a sedentary position and stopping quickly, or switching directions quickly by slowing one muscle group's motion and firing off on another muscle group's motions).