The words man and woman are primarily nouns representing the adult of each sex in the human species, but the two words have other uses, as well.
Man is frequently used as a verb, as in "man the barricades" or "man the telephones," meaning to have someone, not necessarily men, doing a particular job. I don't recall ever hearing woman used as a verb.
The term "man cave" has become popular in recent years to refer to a place where a man can watch a football game, drink a beer or work on a hobby with minimal interruption or interference. There are probably other examples of man being used as an adjective, but I can't think of any. The word woman, on the other hand, is often used as an adjective, even when the word female would be the better choice. There is a National Association of Collegiate Women Athletes and an association called Women Chefs and Restaurateurs. The Contra Costa Times reported in November, "The U.S. Senate is on track to have an all-time number of women members."
I find it interesting that man and woman, as words, have somehow gone off in slightly different directions.