Biasing is the term given to the adjustment of the output devices.
Many people believe that only valve amps are biased, this is a bit of a myth. To understand biasing we need to understand that to make a full wave we need drivers for the plus part of the wave and the negative. This can be the pair of valves you see in the back of your amp, that is why valve amps generally have pairs or quads as their output valves, there are other configurations however this is the most common layout and is known as a Class AB. The purpose of the driver be a transistor or valve, is to convert the low current of the signal into a high current designed to drive speakers.
Due to the losses and construction of a silicon transistor/ MOSFET means that it does not start to operate until it has a minimum of about 0.6V to turn it on. As you can imagine that levels below this do not get amplified correctly and gives the wave a 'knee' curve and non-linear operation as can be seen on the below graph.