LOL
Ahem ... it's not a "ball"(*) indicator but more slip indicator
The purpose is to show if you are flying "coordinated" : using enought rudder to compensate the slip of your plane when turning.
Some plane have 2 :
one in main control panel
the other just under the gunsight because it's hard when aiming to look at the main panel.
Firing uncoordinated (aka sliping) generaly ruin your aiming just like being out of trim.
(*)hint : if you are a man you got 2 if not you have (I hope
) 2 tits