My dentist said I have a bony growth on my lower gum, exostosis. What is this?

Not that unusual. Sounds like an exostosis is benign growths of bone. They are painless and self-limiting but may contribute to gum disease if they become too large. If concerned see your dentist for consultation.
Extra bone. Most often these are on the inside of the lower jaw. They are called tori. If on the roof of mouth it is a maxillary or palatal torus. If on outside of jaw, below gum line on lower , above on upper, then they are called exostoses. It is a benign growth of extra bone. If it is a problem it can br trimmed away by the oral surgeon. Usually not a problem, or simply a nuisance.
Benign bone. An extra deposit of bone, normally a buttressing effort by the body to support teeth when a bite is not balanced. The bone is not pathological but may need to be removed if dentures are needed. Bite balancing (occlusal equilibration) may be offered.
Is it getting bigger. I believe it is your bodies response, buttressing bone, to clenching or grinding. I am also concerned about it on the upper or lower jaw making less room in your mouth for your tongue at night. If it is not getting bigger and is not causing any problems there is no reason to have it removed.
Torus. This is a benign growth of bone, usually on the inside of your lower jaw, or on your palate. They can also be on the outside part of your lower gums.
Just that...bone. Those bony growths are called tori or singular....Torus. They are harmless and don't require any treatment unless they get too big and begin to cause a problem or may be in the way of getting dentures or implants. Simply put....No worry.
Extra bone. It is merely an outgrowth of extra bone. It is completely benign and no treatment is generally needed. One exception is patients who require dentures, where that extra bone may interfere with the seating of the dentures and therefore it has to be removed.