One really simplified way to think of it is as a path. In a mixer, you have all these inputs, a simple bus might take 2 or more mono or stereo inputs and mix them together to one output bus (left and right). This would have a single output bus.
Now if you want to take the inputs and do something to each one (say add eq), you Can send the signal out to an effects bus, then add your eq (and any other effects) then send it back to the output bus and it flows to your output.
Now say you have your main output, but you want to be able to monitor the mix while you are recording via headphones (so someone is listening to the main mix through the output bus, but a singer wants to hear output into headphones in a separate room), well then you might have a second output bus for a headphone mix. With many systems you could even have a different mix for the headphone mix than the main mix- for instance, if you want the singer to hear bass and guitar and drums only, with all that lower in their personal mix, but their vocals louder to make it easier for them to monitor their performance (or quieter so they sing out more perhaps). You might only send some of the mix to that headphone bus. so even though they are all using the same inputs, the main mix and the headphone mix might sound really different.
From there, things can get complicated as you add more and more paths for audio to move through, with sends and returns and aux busses etc.
Daav