What does the no_chdir => 1 mean?

from File::Find manual:

"no_chdir"
          Does not "chdir()" to each directory as it recurses. The wanted()
          function will need to be aware of this, of course. In this case, $_
          will be the same as $File::Find::name.

In other words, it just means that your program will skip the chdir part which is useless for your program (so you gain again some CPU cycles) and, as a bonus, $File::Find::name equals $_, so you'll be able to use:
push @{$files{$name}}, [ $_, $size, int -A _ ];
instead
push @{$files{$name}}, [ $File::Find::name, $size, int -A _ ];

What is the purpose of Cache::MemoryCache?

heh, i told you in my previous post to consider using getpwuid and a caching system instead of pushing all users information into memory. Cache::MemoryCache is just a wellknown module that could be useful for such things. OFC, it your specific case, this could be overworking as your program is too simple and maybe a simple hash cache would be enough. Anyway, I was trying to prepare you for more complicate stuff ;-)
What is being cached? The correspondance between UserIDs and UserNames.
Let's see an example using a simple hash-cache.

my %cache;
find({wanted => \&ab_wanted, no_chdir => 1}, $opt{d});

use Data::Dumper;
print Dumper \%files, \%cache;

sub ab_wanted {
    if (-r _ && -f _){
        $size = int ((-s _) / 2**20);
        if ($size > $opt{s} && $opt{a} < -A _){
            $uid = (lstat(_))[4];
            my $name = $cache{$uid};
            unless (defined $name) {
                $name = getpwuid($uid);
                $cache{$uid} = $name;  
            }
            push @{$files{$name}}, [ $_, $size, int -A _ ];
        }
    }
}
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