Depending on the location, state of the bone and other parameters, anything from mild discomfort to catastrophic failure of the implant and a jaw fracture.

I have four implants, two in my lower jaw, two in my upper jaw. My lower jaw is basically stone, an extremely hard bone even by usual lower jaw standards; the dentists (plural, as one was unable to finish the job) drilling into it destroyed a few drilling bits doing so. I have never had any problems with the lower jaw implants. That bone can take almost anything in stride.

My upper jaw, on the other hand ... very delicate, just enough bone left for the implants to work, and I learnt to be careful about biting into anything harder with them.