male: of the male sex, as opposed to female, whether of people or of animals
This word names a creature's sex. It marks something or someone as male rather than female, and it does so for both people and animals. Unlike the everyday word for a grown man, it is not about adulthood, social standing, or being a husband. It is the plain category "male," which is exactly why it pairs again and again with its opposite, נְקֵבָה, the word for "female."
Because it is a category word, it does the work that sorting and counting require. It tells you which infants are circumcised, which people are numbered in a census, which firstborn animals belong to God, and which animal is acceptable on the altar. In each case the point is the same fact, sex, applied to a different setting.
The two senses below, the male person and the male animal, are not two different meanings. The word means "male" in both. They are kept apart only because the surrounding text is doing different things: in one the male is a person being counted or marked, in the other the male is a beast being set apart for sacrifice or as a firstling.