I am seeing both of them used in this script I am trying to debug and the literature is just not clear. Can someone demystify this for me?
From man perlsub:
Unlike dynamic variables created by the local operator, lexical variables declared with my are totally hidden from the outside world, including any called subroutines.
So, oversimplifying, my makes your variable visible only where it's declared. local makes it visible down the call stack too. You will usually want to use my instead of local.