In its most general sense, the bus in a mixer is a path where electronic audio signals travel. On a mixer, there are several different kinds of buses, depending on the kind of mixer that's being used. These can include the stereo, group, PFL, auxiliary and individual channel buses.
Mixers come with a certain number of input channels where musical instruments or microphones can be connected. The number of channels is designated by and even number: 4-channel, 8-channel, 16-channel, and so on. The majority of those channels are mono inputs. That means that the audio signal is traveling down one path only, passing through other controls before it gets to the volume fader or knob.
As the audio signal travels down the single mono input bus, it can be affected in a couple of ways. The most common ways are through the board's EQ (equalization) and pan controls. The EQ controls adjust the frequency of the incoming sound. The two most common controls are bass and treble, which are represented on a mixing board as Hi and Low. Some mixing boards also have Mid, for mid-level frequencies. Adjusting the control up or down, the audio engineer can cut or boost the frequencies of the signal. Pan (short for panorama) controls allows the adjustment of the sound more to the left or more to the right in the audio spectrum. This spreads out the sound to give the illusion that certain instruments are in certain parts of the room, simulates a musical performance to a greater degree and creates space for the signals to breathe and not compete for room in the mix, which can result in something that sounds sonically harsh and busy.
Stereo refers to the audio spectrum between two speakers. A channel that has a stereo bus has two independent outputs on the mixing board and is where all the mono signals are routed. Depending on the panning, more of the signal may go to the left or to the right speaker.