Hi @Jennifer31, if he says he booked he will have a confirmation/reciept and a reference number. And you would have the booking in the Reservations section on your AirBnB account. If he can't produce evidence of the booking and you don't have a reservation either then you should not allow him into your home and he will need to contact AirBnB to try to sort it out.
Click on Reservations and you will see whether or not he is showing as a booking for you.
As already said, if it's not there then advise the guest to contact AirBnB as you have no booking for him. Do not, under any circumstances allow the person in to your home - it could be a scam or worse.