personal remark/comment an intentionally offensive remark about someone's character or appearance example : Did you have to make such a personal remark about her new haircut? http://dictionary.cambridge.org/dictionary/british/personal

It would depend how this was used. Personal generally means something that should be exclusive to one's own self and perhaps their close friends. If someone said "That was a personal remark," it could mean that you were being invasive, or rude, by something that you said about that person. If you said "That was a personal remark," it probably means you said something, and you want the other person to understand that you were speaking about yourself. It could be other things as well.

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