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A differential signal is a signal that requires two traces having different potentials (voltages). The receiver looks at the difference in potential between the two to determine the logic level. You can specify the "differential impedance" of the two traces (wires) when laying out a PCB board. A single ended signal is a single trace whose voltagel is measured relative to ground (or common reference). A single ended impedance (with respect to a copper (i.e. ground) can also be specified when laying out a PCB.
Usually single ended signal is refered to earth, and you transmit it in the unbalanced mode of communications that is te signal is refered to earth and it travels trough only one line, it is unexpensive because only one line of communicaton is used, but it is affected by noise and it is difficult to eliminate the noise.
Differential signal is not refered to earth, it is refered to the other line, so the signal travels trough the two lines differential mode, that is balanced mode of communications, and of course is more expensive, but when noise afect the signal it add in common mode. The diffamp amplifies the differential mode signal and attenuates the common mode signal.
The arguments relating to the effect of symmetric circuits:
1. Isolation from supply related effects. So every effect applies to a pair but if you signal is expressed as difference within each pair. It make in effect a separate dimension of signal processing. In reality interaction happens because a pair is not perfect and if a pair is driven by a signal it gets sensitive by the common mode signals.
2. Second order distortion gets canceled in pairs. That help to improve linearity.
The most useful argument for symmetric circuits is to get rid of device related offsets in DC processing circuits. So a pair could have processing depend bias but because of the interpretation of a difference it get canceled.
The earliest application of symmetric DC processing circuits was an opamp with a triode pair.
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