What does it mean to have a dental implant "fail"?

The implant did not : The implant did not integrate with the surrounding bone. Many factors could cause this.

Depends: There are levels of failure with the worse being the lack of fusion to the bone resulting in its removal. If there is pain and pus associated with it then the implant is failing and should be looked at asap because this is an indication of failure. If you have concerns seek immediate evaluation by your dentist.

No integration: Implant failure means no integration occurred between the implant and bone.

Bone did not grow: A failed implant means that bone did not grow around the implant so it is loose. It could be that skin grew down the sides of the implant as well, or finally an infection occured.

No bond with bone: Dental implants "fail" at predominantly two times: first, when they don't bond to the bone in the first place (if the bone is not sufficient in quality or quantity) or second, when the implant bonds to the bone but when teeth are put on the implant and the implant loosens because the bone is not strong enough to withstand normal chewing forces. International success rates are very high.

Did not integrate: Typically this means that the bone did not grow to the implant surface in order to lock it into place. So, the implant becomes mobile (loose) and will work its way out or will need to be removed. Can also "fail" over time due to excess occlusal (biting) forces, bone/tissue infection, and sometimes for unknown reasons. Success rates are in the high 90's %.

Failing and ailing: Failing implant: implant to bone contact could not be establish, resulting in loss of implant. Ailing implant: inadequate implant to bone contact established, causing complications such as gradual bone loss (vertical or horizontal) after occlusal loading, mobility, bleeding upon probing, peri-implantitis, etc... # 1 reason for implant failure: inadequate bone height and bone width.

Failed to "bond": I would say the dental implant did not heal properly. The jaw bone for some reason failed to fully attach itself and bond to the tooth. Or for some reason an infection may have situated itself around the dental implant or associated gum tissue.

Osseointegrate: When the bone heals successfully against an implant we say it "integrates." lack of integration is a failure.

Inadequate stability: When a dental implant 'fails', it basically means that the implant did not have enough bone grow in contact with the implant surface to make it stable and immobile. Implants can fail before they are restored, or after they have a crown, bridge, etc. On them. Medical conditions, infection, poor surgical technique, poor home care, and poor bite can all contribute to an implant failing. Stay strong!

Mobility ; function : Initially an implant is considered a failure if it's surrounding bone does not integrate/attach to it. However, even osteo/bone integrated implants can fail from excess cement causing supporting bone loss, poor angulation resulting in lack of function or unacceptable esthetics.