In short they reduce friction between moving parts, helping keep your reel moving freely and nice and smoth under loads created from your drag and winding.
Let's say you had 2 of the EXACT SAME reels but 1 was a 2 ball bearing reel and the other a 5. If you spun them both freely at the same time and speed then let go, the 5 ball bearing reel should spin longer than the one with 2. Also the 5 ball bearing reel should be smoother than the 2 under the same drag load. Lastly as the same reel, if both were constantly winding you would expect the 2 ball bearing reel to give in first as more friction and heat is created by the moving parts due to having less.
So then how many do I need in my reel you ask? Well I advisee people if you dont really fish much then a 2-3 ball bearing reel would suite but for the person fishing a bit or for larger fish then go 5+ to help with life span/wear.
Lastly the amount of ball bearing in a reel does NOT always reflect quality of build but more so how smooth it should be and even the best reels will stop working right if not looked after well.
The Sydney Marine Man