Walking through the code after a bit of reformatting, with some comments:

# Use a hash slice to copy all the keys in the symbol table to %s,
# and set each key to undef.
@s{keys %::}=();

# Bless a hashref into the current package, thereby creating
# AUTOLOAD and DESTROY entries in symbol table.
bless{};;

# Pull out any keys in %s that are not in %:: (AUTOLOAD and DESTROY),
# sort them, and take the second element (DESTROY).
# Assign an anonymous sub to the DESTROY typeglob.
*{ (sort grep{ !exists $s{$_} } keys %:: )[1] } =
sub
{
    $n = 0.5;
    {
        # Print a carriage return (sends cursor to beginning of line).
        # Split the JAPH text into single characters, then for each
        # character, choose a random number between 0 and 100,
        # compare to $p and print the character or a space.
        # Note: as $p increases there is a better chance of
        # displaying the character (and visa versa).
        # Question: is the comma in the JAPH text intentional?
        print "\r", map { rand(100) <= $p ? $_ : ' ' }
                        split //, "Just another Perl hacker,";

        # Stop loop when $p < 0 ($n is 0.5 or -0.5, so always < 1).
        $p < 0 && $n < 1 && last;

        # Use $n to increase or decrease $p by 0.5
        # $p increases from 0.5 to 110.5, then decreases to -0.5
        $n *= $p > 110 ? -1 : 1; # change sign of $n if $p > 110
        $p += $n;                # increase/decrease $p by $n

        # Use the four-arg form of select (ready file descriptors):
        # $q is undef, and the timeout value is set to 0.04 sec
        # This is equivalent to sleep 0.04 with better resolution.
        select $q, $q, $q, .04;

        # Redo this block
        redo
    }
};

# This can be rewritten as 'bless \$0; $| = 1;'
# Bless the scalar $0, but since we didn't save a reference to the
# newly created object it is immediately destroyed - the DESTROY
# method is called on the object, and the sub above is executed.
# This can be observed by explicitly declaring an alternative
# DESTORY method, or by adding 'print "destorying $_[0]\n";'
# to the first line of the subroutine.
bless \$|++;
[download]

Update: the original code was tweeked, but I don't think it changes this explanation.