A single-ended system is a system with a single output referred to the common terminal (ground) (voltage case).
A balanced, or differential, output consists of two terminals, Vout1 and Vout2, and the output voltage is measured between them. We have in this way Vout=Vout1-Vout2. Let us define now the common mode voltage, and the differential voltage. Vc=(Vout1+Vout2)/2 and Vd=Vout1-Vout2. Vd is your useful signal, while the common mode is the "middle level" of the output.
The common mode have to be defined, but carries no useful info.
We can also write Vout1=Vc+Vd/2 and Vout2=Vc-Vd/2. We can easily notice that the outputs vary around the common mode simmetrically.
The balanced output has some clear advantages: equal signals (same phase and amplitude) coupled to both the terminals (radiated signals, interference, EM) are rejected and Vd is not affected by them. In the single-ended configuration you will suffer of them. So balanced configurations are more accurate.
You can find this infos in every basic electronic book. However, i found an explanation googling (definitions and transmission considerations):
**broken link removed**
Now take into account amplifiers and op-amps.
We surely have to make a distinction in this case, too. We have single-ended amps (single-ended output, single or balanced input) and fully differential amps (balanced input and output). The advantages are quite the same. Fully-diff are employed in switched capacitor network, for rejecting charge injection, and generally wherever we need high precision and rejection of common mode disturbance and interference. The design of a fully differential op-amp presents some different aspects with respect to the single-ended: we need to set the output common-mode voltage with special circuitry.
You can find infos in analog IC books (i suggest Allen or Gray or Baker).
This is only an intro, if u have questions ask!
Hope it helped (if so press helped me !
)