1994 Buick Century Horn(s) Non-working

My car has two horns. When I push one of the horn buttons, mounted on the steering column on either side of the air bag, the only sound I hear is a clicking noise from under the dash; left side of the steering column. The sound comes from a small white square plastic box with holes on one side.
Is this a relay similar to the turn signal flasher? Meaning that replacing this piece may solve the non-working horn problem similar to when the flasher goes bad? Any suggestions for getting my horn(s) to work are greatly appreciated!
I was nearly hit when a truck backed up and my horn was unable to warn him.
Thanks for your help!