The numbing shot is simply a local anesthetic that temporarily deactivates your nerves so that you do not feel pain when your teeth are being pulled or being worked on.
The most common ingredient and type of medicine in the numbing shot or numbing injection used by dentists to numb your mouth and gums is Lidocaine.
It's a local anesthetic that just temporarily shuts down your nerves so that the pain will not be felt because if the nerves were activated you'd feel pain when a tooth is being extracted or your teeth are worked on.
The numbing shot is a pretty safe anesthetic and will eventually wear off after a few hours to a day depending on how much of the injection was given.