You can use "he" to refer to anything that's biological male, and "she" to anything that's biological female. "It" can refer to anything that's not human.
As you can see, there's an overlap when it comes to animals. A cat is either male or female, so you can call it "he" or "she", but it's also not human, so you can also call it "it".
It would sound strange to call a random cat "he" or "she". If you randomly pointed at a stray cat and said "He/She is...", the listener would assume you have some familiarity with the cat, since you know what gender it is. As a general rule, always use "it" when talking about an animal, except when it comes to pets. Even when the gender of the animal is obvious (e.g. male lions have manes and female lions don't), we would still usually default to "it". You'd call your own "cat" "he" or "she" since you'd (hopefully) know what gender your cat is.
If you're talking to someone else about their cat, you can just say "it", but if you hear them say "he" or "she", you should use whatever pronoun you hear.
E.g.
A: You have a beautiful name. What's its name?
B: She's called "Becky".
A: She's very beautiful. I see you have another cat. What's its name?
B: His name is Steve.
A: He's a very fat cat.