Please put code here inside <code>...</code> tags, that way it's easier to read for us.

push (@{$ttys{$user}}, $tty );

There is a hash called %ttys. This statement access the item of this hash with the key $user, dereferences it as an array (that's the @{ ... } part) and pushes the variable $tty onto this array.

You need to do such a thing if you have multiple key/value pairs with the same key.

A user can have allocated several terminals (ttys), so for a mapping from user to terminal you need to account for the possibility of having more than one terminal per user.

See also perlreftut and perldsc.