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?
"my" variables are visible in the current code block only. "local" variables are also visible where ever they were visible before. For example, if you say "my $x;" and call a sub-function, it cannot see that variable $x. But if you say "local $/;" (to null out the value of the record separator) then you change the way reading from files works in any functions you call.
In practice, you almost always want "my", not "local".