What is a bone density scan test, and does it require radiation? Is it harmful?

Yes and no. Yes it requires radiation. The bone mineral density test (which is not a "bone scan" which is something entirely different) requires x-radiation. But no, it is not harmful in and of itself. The radiation dose is around 1/10 the dose from a chest radiograph. That said, radiation doses are cumulative, so each dxa adds a little to your total dose accumulation and risk.
Safe. Bone density scans usually use radiation to measure the density of bone. The dose of radiation is much less than that from a chest x-ray. It is not considered harmful.