<p>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?</p>

Well Google really works for you on this one:
http://www.perlmonks.org/?node_id=94007
From the link:
Quick summary: 'my' creates a new
  variable, 'local' temporarily amends
  the value of a variable.
ie, 'local'
temporarily changes the
  value of the variable
, but only
within the scope
it exists in.
Generally use my, it's faster and doesn't do anything kind of weird.