An unbalanced connection uses two wires; one wire carries the signal, and the other wire in the ground. A balanced connection is a three wire system, where 2 wires pass signal (positive in one and negative in the other), and the third wire is the shield, or ground.
Balanced connections are almost always used with low impedance microphones, because balanced connections are more resistant to noise, and are by far the preferred connection for professional audio. The XLR connection is the most popular balanced connection for several reasons. It has three conductors, it is shielded, and can lock into place, and also, the ground connection connects first to avoid pops.
Unbalanced connections are normally used for high-impedance microphones and pickups, and sometimes for low impedance consumer microphones. The unbalanced system is susceptible to noise, and is generally not preferred in professional work. The most common unbalanced microphone connector is the 1/4-inch connector. For microphones, balanced connections should be used wherever possible. Sometimes this will require the addition of an external transformer at the mixer input, but the advantages in noise immunity and reliability justify the expense