I had a cat that used to keep it's mouth open and the vet told me that the reason my cat was keeping it's mouth open was because the cat is investigating it's surroundings and keeping it's mouth open helps with that.
The cat is considering the scent around it and sucking in the air which is then transferred to the cats Jacobson's organ which is also known as the vomeronasal sac and can be found behind the teeth in the roof of the cat's mouth