According to the search results, "mog" has multiple meanings, depending on the context. Here are the different definitions:

• To move away or depart, usually followed by "off" or "on".
• To walk or move along gently, slowly, and steadily.
• A variant of "moggy," which is a pejorative term for a cat.
• An acronym used by girls to refer to a "Man of God".
• In internet slang, "mog" can mean to be significantly more attractive than someone or something, or to dominate in appearance.

Its important to note that some of these definitions are dialectal or slang, and may not be widely recognized or understood.