I'm semi new to Baitcasters. I'm wondering why people use 20-60 lb test when the reel is rated for 10-14 lb test? Please help!

They give a pound test and the number of yards the reel will hold for that pound test.  Has nothing to do with line rating for the reel.  Also these figures are almost always for mono lines not braid.  People use 20-60# braid for several reasons.  One being it requires a lot heavier braid for a given diameter.  50# Sufix 832 Ghost is equivalent to 12# mono.  Therefore if the reel says 12# / 135 yds, it will hold 135yds of 50# 832 Ghost.  As you can see it pays to use a cheap mono backing with braid.  

 

Another reason is for fishing in heavy cover.  My brother-in-law uses 40# braid on all his spinning reels because he is throwing back into lily pads a lot and doesn't like losing lures.  Braid has very little abrasion resistance so if you are fishing in an area where you need an abrasion resistant line...and are using braid...then you'd better increase the size of the braid.  You might be able to land a fish in those circumstances with 50# braid whereas 20# braid might be weakened enough (from abrasion) to break on the hook set.