Compound gearing allows you to get the same gear ratio as a 10t>80t (8:1) without having to use a huge 80 tooth sprocket on the rear axle.
Say if I had some 10" tall tires, but needed an 8 to 1 ratio (10>80) I wouldn't be able to get that ratio because the axle sprocket would be like twice the size of the tire. With compound gearing you can take a small drive sprocket to a jackshaft with a larger sprocket, and then on the output of the jackshaft have a sprocket smaller then the one on the input side, and a lot smaller axle sprocket than the 80 tooth that would be needed.
Here, play around here
http://www.compgoparts.com/TechnicalResources/JackshaftRatioCalculator.asp
And it'll show you how compound gearing calculation works (plus I'll be honest, I don't wanna explain it while inherited lol)
Basically it allows you to get ratios you couldn't get because of space/size limitations. Or it allows you to get more clearance from your axle sprocket.