Think of a bus as a metal rod inside your mixer. Now, you can put a signal on this rod at some point and take it off at another. For example, you can put one or more channel inputs on the rod (effects send), then take them off and send the signal to a processor. Then you can take the signal out of the processor and put it back on another rod (effects return). If you want to handle a particular group of inputs all together, say vocals only, you can put the vocal channels all on their own rod (a sub group). You could then send the signal on that rod to the main or sub-group rod.
Another example would be for monitors. For one monitor mix, you might just put all the vocals on one rod (monitor aux 1, let's say) and send it to the auxiliary 1 out. Certain instruments might go onto another rod then go to auxiliary 2 out. Monitor sends usually do not return to the mixer, they just go out to the monitor amp.
Now just go up and change the word "rod" to "bus."
So an 8-bus mixer has eight different rods you can use to put signal on and take it off. Some for effects sends and returns, some for monitor mixes, some for grouping channels, whatever you want.
On the board itself, these are called auxiliary busses, or "aux." Some boards will have a couple auxes labeled "monitor" and/or a couple labeled "effects." Usually, the monitor channel sends will be situated in the circuit such that the monitor volume is not affected by the channel's volume fader (hence, "pre-fader"). Usually, the effects outputs will follow the volume of the fader ("post-fader"). Most good boards will have at least some of their busses switchable pre- or post-fader.
Clear as mud, right?