One theory for why cats chirp is that it is a way that mother cats tell their kittens to follow them. Another theory says that it is an exaggeration of the movement that the cat uses to kill prey. It may be a noise of frustration or excitement, or it could be a way for cats to mimic the sound of their prey.
Cats make this chattering or chirping noise by opening the mouth slightly, pulling the lips back and opening and closing the mouth rapidly. The noise comes from a combination of lip smacking and teeth chattering.
The Humane Society of the United States indicates that the chirping or twittering noise that a cat makes could be an exaggerated version of the killing bite that cats make when they are trying to work their teeth through the neck of their prey to snap its neck. The Pet Assure Newsletter suggests that it might be a way for cats to vent their excitement at seeing potential prey and frustration at not being able to catch it.
Catster proposes that cats are able to listen to their prey and purposely mimic them in order to lure them into a passive state. This theory is supported by cats' vocal agility and cunning minds.