A person who is remorseless doesn't feel any guilt. If you're remorseless, you don't feel bad at all — even if you've done something terrible.
When someone is remorseless, that person has no feeling of pity for people who have been hurt. If you're remorseless, you have no conscience — essentially, you're cruel and ruthless. A remorseless killer doesn't care about her victim, and a remorseless critic doesn't worry about hurting someone's feelings with his harsh words. Remorse is regret, and it's rooted in the Latin word remordere, "to vex or disturb," or literally, "to bite back."