Meaning of balanced transmission line?
The two signal lines are mirrored around a central reference point - often but no necessarily ground. When one is 'up" relative to the reference point the other is ":down" by an equal amount. The mean level is always zero relative to reference.

In a digital system the driver applies +v/-V for eg logical 1 and -V/+V for logical 0.

This is compared to an unbalanced system where one line may be considered the reference (often ground) line and the other swings relative to it. eg in the RS232 system logical 1 = -12V nominal and logical 0 = +12V nominal. When a 1 is sent the legs ae at -12/0 and when a 0 is sent the legs are at +12/0.

A balanced system is inherently more immune to noise. If fed via  a twisted pair, noise induced into the pair is of the same amplitude in both legs and the differential signals still have the same amplitude +/- or -/+ relative to it. So noise levels can be greater in magnitude than the signal and the system will still work.

Voice telephony in standard telephone systems use analog balanced signals. Max transmit level is usually about -10 dBm where 0 dBm = 600 mV in 600 ohms = 1 mW. Customer end of line signals may be 10-20 dB below that and still work 'after a fashion". Despite this low level of signal you can have many volts of induced (usually 50 Hz or 60 Hz mains) noise on a cable pair and not hear any "hum.
 Imbalance the line just slightly and ALL you will hear is hum.