$num_tries = ( isset( $num_tries ) ) ? ++$num_tries : 0;
Basically, it says:
If $num_tries is set, then increment $num_tries by 1 and then returns $num_tries, otherwise, set $num_tries equal to the value of 0.
Written using a standard if/else, it would look something like this:
if(isset($num_tries)) {
$num_tries = ++$num_tries;
} else {
$num_tries = 0;
}