How does a tv antenna balun work?

It is a small transformer that allows you to properly connect a 300 ohm "balanced" antenna to 75 ohm "unbalanced" TV set. It works by allowing a "balanced" antenna to combine its outputs (it has 2) to the single input of the "unbalanced" TV (the center conductor of the coaxial cable).

A common use would be to connect a pair of rabbit ears to the cable TV input of your TV.