What is it about the value '255' that allows the program to work correctly ?

255 has all ones. Thus if the program tests the same bit and prints 1, 8 times it just looks like it worked.

It didn't. Any value that has the first bit set will also produce a 1:

say 253 & 2 <=> 0;;
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Using the OPs original code, the fact that only the first bit is being tested becomes obvious when you enter a 1:

C:\test>perl

#!/usr/bin/perl -w
use strict;
use warnings;

print "Enter decimal number less than 256:";
my $decimal;
$decimal=<STDIN>;
#chomp $decimal;
print $decimal & 128 <=> 0;
print $decimal & 64 <=> 0;
print $decimal & 32 <=> 0;
print $decimal & 16 <=> 0;
print $decimal & 8 <=> 0;
print $decimal & 4 <=> 0;
print $decimal & 2 <=> 0;
print $decimal & 1 <=> 0 ;
^Z
Enter decimal number less than 256:1
11111111
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And the fact that 255 appeared to work, is just coincidence.