Maybe it will be more easy to understand...
$my_date = '2008-02-16 12:59:57';
$one_day_after = date('Y-m-d H:i:s', strtotime('2008-02-16 12:59:57 +1 days'));
if($my_date < $one_day_after) {
echo $my_date . " is less than 24 hours ago!";
} else {
echo $my_date . " is more than 24 hours ago!";
}