Using "he" or "she" for an animal not a person?

Is it possible to use the personal pronoun subject he or she for a nonhuman animal according to their sex?

One of my friends said that there is a possibility of using it for animals. My concern is that my friend did not give me the real explanation of why and how to use the pronoun in this case.

Yes, animals of a given gender can be referred to using he or she as appropriate. For example we might say

The female dog runs across the field. She is fast.

However, when referring to an animal of unknown gender, it is acceptable.

The dog runs across the field. It is fast.

This is in contrast to people. If a person is of unspecified gender, one is more likely to use he or she. In fact, the correct gender-neutral third-person singular pronoun to use for a person is rather controversial, as shown in this discussion.

Regardless, for animals the answer is fairly clear-cut: use he for male animals, she for female animals, and it for animals of unspecified gender.