An unbalanced signal is carried by a cable with only two cores ('hot' or signal carrying, and 'ground' or earth). It is very vulnerable to interference as it travels along an unbalanced cable - for example electrical noise from nearby power supplies. It therefore cannot travel very long distances without becoming degraded.
A balanced signal, by contrast, requires a three-core cable ('hot' and 'cold' carrying the signal and 'ground' carrying the earth). The signal in the 'cold' core is phase-inverted (i.e. the waveform is turned upside-down). The receiving device need only re-invert the cold signal and add it to the hot signal - any interference will cancel itself out, resulting in an accurate transmission of the original signal.
To balance a signal, we need a device called a DI, or DI Box. This simply takes the input from the unbalanced signal, a jack cable usually, and converts it to a balanced signal, usually carried by an XLR. Two kinds of DI Box exist - passive and active. Active DI Boxes require a power supply - though often phantom power can supply the necessary power.
For more details see: