local gives a value to a global variable.
While the localization is in effect the original value
is unavailable. When it ends the old value is restored.

Update: Value is the wrong word above. The technical
term is thingie. local attaches the name to another
thingie for a while

my creates a new variable which may incidentally
have the same name as a global variable. This is the common
type of declaration as in C or C++.

Usually you want to use my.

You can't my %hash; local %hash; but
it is possible to my %hash; local $hash{key} = 1000;
I haven't used or examined this usage though.

I don't, GASP, have perl on this machine, so this is untested, but will demonstrate the important differences
between lexical and dynamic scoping.

$var =1;

{
   my $var = 2;
   print "\$main::var >$main::var<\n";  
   print "\$var >$var<\n"; 
   &show_var;
  # my var doesn't exist outside this scope
}
{
   local $var = 3;
  # local var gives $main::var a temporary value
   print "\$main::var >$main::var<\n";
   print "\$var >$var<\n";
   &show_var;
  # local var ceases to exist when we _leave_ this scope
}
print "\$var >$var<\n";

sub showvar { print "showvar($var)\n"; }
[download]