If the input were 'y', the first part of the || would be false, but the second part would be true. For an input of 'n', the first part is true while the second is false. Any other input, both parts are true. The only way to avoid the loop if the input is simultaeneously 'y' and 'n'. Only Damian can do that.

I would use shortcut returns to drastically simplify the condition:

sub continue_yn
  {
   print "Do you wish to continue the installation (Y/N) : ";
   $yn=<STDIN>;
   chomp $yn;

  LOOP:
   while ( 1 )
     {
      last LOOP if lc($yn) eq 'y';
      last LOOP if lc($yn) eq 'n';
      print "Invalid option, please enter an Y or N : ";
      $yn=<STDIN>;
      chomp $yn;
     }

   print "Valid option entered";
  }
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Or use a hash to specify the set of valid inputs.

Readonly my %VALID_CHAR => ( y => 1, Y => 1, n => 1, N => 1 );
sub continue_yn
  {
   print "Do you wish to continue the installation (Y/N) : ";
   $yn=<STDIN>;
   chomp $yn;

  LOOP:
   while ( 1 )
     {
      last LOOP if $VALID_CHAR{$yn};
      print "Invalid option, please enter an Y or N : ";
      $yn=<STDIN>;
      chomp $yn;
     }

   print "Valid option entered";
  }
[download]

WARNING: not tested. Provided for concepts, not cut-and-paste.