Well, depends on what you want to do.
I quote, perldoc -f my:

A "my" declares the listed variables to be local (lexically) to the enclosing block, file, or "eval".

Let the code speak:
Run this code, study this code... :)

#!/usr/bin/perl
#Is you is, or is you ain't, my foobar?
#The dope on  scope.
baz(); #call baz.
sub baz {
 my $foobar="I feel Baz!\n";
 print $foobar;
 #$foobar is now lexically scoped for 
 #the whole subroutine block.

 if (1) { #This is another block, it belongs to if.
 my $foobar="I am the FooMan!\n";
 print $foobar;
 #$foobar is now lexically scoped 
 #for this if block;
 }
 print $foobar;
 if ("I own several pairs of pants") {
 #That ^^^^ is another if, and this is its block
 my $foobar="I am the BarMan!\n";
 print $foobar;
 #$foobar is now lexically scoped for this if block;
 }
 print $foobar;
}
[download]

Now, what I would do for your little file opener is

sub openFile {
 my @entries; #is now lexically scoped for the entire subroutine;
  if ($file1) {
    open FH, "$file1" or die $!;
    @entries = <FH>;
    close FH;
  }
  if ($file2)  {
    open FH, "$file2" or die $!;
    @entries = <FH>; #Replace all the entries? what?
    close FH;
  }
}
[download]

Get it? Also, there are many flaws with the openFile code, but I digress
Have fun!