It's about half-obfuscated, deliberately. I didn't really care which magic variables I used, as they were mostly all good candidates (don't need to be declared, a first year student probably wouldn't know anything about them).

Here's my explanation:

@ARGV=();

I use the magic input operator in a moment to read from STDIN. This'll break if @ARGV has anything, so I clobber any command line arguments.

$; = "%2u * %2u = %u";

I'd have to look up $; to see what it does. It doesn't break anything, so why not use it here? This is just a format string for printf. It's also the source of the apparent bugs jptxs and tilly mention.

($_ = $. = <>);

A little bit of misdirection here. Would a beginning programmer know about $. or the magic input? I think not.

do { chomp; $! = !(defined($_)) } while ($|);

This just gets rid of the newline on $_ and sets $! to 0 ($_ is most likely defined, so I negate the result of that check). $| is 0, so it only executes once.

print join($/, map{ $!++; sprintf($;,$!,$_, ($_ * $!)) } (($.) x 10));

Here's the real meat. First, we create a ten-element list of the input. There's another subtle bug that doesn't hurt any, because $. hasn't been chomped. Perl does what I mean, though.

Next, we increment $!, which we use in the multiplier. It's at zero to start, so we need to get it to 1 before looping.

The map returns a list of strings from sprintf, with the format slots filled. The join puts them together with the contents of $/ (a newline, as we haven't messed with it) and they're printed.

There you have it. A mess of punctuation with concepts a beginning programmer wouldn't know but bugs he'd be likely to produce. Now I have to go take a shower.