An ad hominem remark appeals to personal feelings instead of logical reasons. If you're debating labor laws and you criticize your opponent's extra-marital affair instead of engaging his ideas, that's an ad hominem attack.
Ad hominem is a phrase from Latin which means "aimed at the man." It's almost always used to describe a way of arguing or criticizing that ignores the larger issues at hand and just attacks someone's character. Unfortunately, political battles in the media often boil down to ad hominem attacks instead of thoughtful debate.