A "bus" in a mixer usually refers to the amount of submix channels it has. In a 4-bus mixer you select each channel to go to one or two of the 4 submix channels, and then you mix these 4 submix channels together to stereo.
An 8-bus simple has 8 of these channels instead of 4. With an 8 bus you therefore can mix say, 32 channels onto 8, where 1-2 is the drums, 3 the bass, 4 the lead vocals, 5-6 guitars and 7-8 other stuff. That way you can change the levels of the drums without having to touch all the sliders for the different drum channels.
A bus mixer is also useful if you want to record many sources at once to a multitrack, you then record each bus to a recording channel.
Well, that's the short version, at least.