From perldata:

The length of an array is a scalar value. You may find the length of array @days by evaluating $#days, as in csh. However, this isn't the length of the array; it's the subscript of the last element, which is a different value since there is ordinarily a 0th element.

The syntax $#{ ... } extends this idea: it interprets whatever expression is between the braces as an array reference; dereferences it to get an array; and returns the subscript of the last element. For example:

#! perl
use strict;
use warnings;

my %animals =
(
    pets => [ qw( cat dog hamster ) ],
    non  => [ qw( rhino   giraffe ) ],
);

for my $i (0 .. $#{ $animals{pets} })
{
    print "$i: ", $animals{pets}->[$i], "\n";
}
[download]

Output:

 1:43 >perl 857_SoPW.pl
0: cat
1: dog
2: hamster

 1:43 >
[download]

But note that, as Cody Pendant says above, it’s generally better (where possible) to dispense with array indexes altogether.

Hope that helps,