Transfomation of impedance using a balun
To clarify your confusion, some transformers have isolated primary and secondary windings. Some don't and have only one winding with a third tap-off point. These are cheaper to manufacture and can be used where isolation is not required. In power transformers they're often used to step the mains down say, from 230 V to 115 V or similar.







simulate this circuit &ndash; Schematic created using CircuitLab

In your case you have a balanced signal which should feed into a balanced load. The balun provides such a load and the two halves of the balanced signal contribute to driving the unbalanced output. Notice that since you only have half the voltage on the output it will be able to deliver more current so its output impedance will be lower than the balanced signal.

I hope that helps.