How to use common mode choke inductors? (differential vs common mode)
Chokes are used to suppress noise, i.e. to prevent noise and other EMI both from entering and going out of some piece of equipment.

What is usually referred to as common mode noise or as differential mode noise are simply two modes in which noise can be coupled conductively (i.e. through wires) into the piece of equipment.

This document explains in more detail the issue.

Essentially common mode (CM) noise is an unwanted signal which couples into both line conductors in the same direction, whereas differential noise is coupled into a single conductor. For simplicity I'm talking about noise coupled into mains line here, where common mode chokes are frequently used, but the same problem arises whenever some wire comes out of an apparatus, for example the leads of a multimeter, an oscilloscope probe or even the USB cable connecting an external HD to the PC.

Common mode chokes usually have two separate windings which are each put in series with each line conductor. These two windings are wound on the same ferromagnetic core in a way that exploits the different path that power line current and CMN currents take in the circuit.
Therefore the choke presents very little impedance to the power line current, whereas common mode noise currents see each winding as much higher impedances, and this attenuates the amplitude of the noise.

Another interesting document is this application note about line filters in switching power supplies.