Differential inputs go into a true instrumentation amplifier (also called a differential amplifier). For each input signal there are two signal wires, one labelled + and the other -. The measurement is the difference in voltage between the two wires. On the socket there is a third connector which allows these signals to be referenced to ground. The two wires go into separate high-impedance amplifiers which monitor the voltage between the input and ground. The outputs of the two amplifiers are then subtracted to give the difference between the + and - inputs, meaning that any voltage which is common to both wires is removed.
The ability of the instrumentation amplifier to obtain the difference between the + and - inputs whilst rejecting the signal common to both is defined by the common mode rejection ratio (cmrr) and the common mode range.
You can use differential inputs in single-ended mode by shorting one of the signal wires (usually the - input) directly to ground. Single-ended inputs are suitable for signals that are of good size, 100 mV full scale or above.
A common problem when using differential amplifiers is neglecting the connection to ground. For example a battery might be connected between the + and - inputs. The two input amplifiers then try to monitor the voltages + to ground and - to ground. Unless some connection is made between the battery and ground these are undefined quantities and may well be too large for the amplifier to handle.