You’re chatting with a friend when another person walks in. You both don’t know this person, so you say to your friend, “Who is that?” He looks at the person and goes to the fridge to get some beers.
That is a relative pronoun that can refer to people, animals, places, things, or ideas. It can also be used to refer to someone who has been mentioned before. When you use that, it’s important to make sure the person or thing is actually present in the room or somewhere nearby. Otherwise, you’ll confuse your reader.
The person who is that you’re referring to should be in the same place as you, or at least within sight. If you’re describing a person that’s not with you, or a person who has died, you can use a different form of the question: “Who was that?”
In the past, there were a few rules about when to use who and when to use who’s or whose. The Chicago Manual of Style allows the use of who for people and animals, but AP style and APA style suggest that who is only to be used for animals with a name. In most cases, however, who is the proper pronoun to use when talking about animals and inanimate objects. The only exceptions are if the animal has been named before, in which case you should use whose or its. Who’s or whose is used to refer to the possessive of an object, not its subject.