The B wire is the call for heat changeover valve in a heat pump system. If you have a conventional heat system (gas or oil), tape it off and forget it. If you do have a heat pump system, you need either B or O call.
Do not go by wire color. Make sure it was/is attached to B terminal on the old t-stat. Sanity check: see if the B wire is even attached to the heater/furnace (probably not).