GPUMAX is a service. It allows you to route your miners through the service so that you still mine at your normal pool, but only when there is no public work. When public work is available, then your miners are working on the public work at a pps that you set in your account.
the public work comes from people who purchase shares at a rate higher than the standard pps rate at other pools.
Which is where the confusion comes from. Most people have problems trying to figure out why someone would pay more for a bitcoin than you would get back. (ex. pay 1.2btc for 1btc).
The thinking about it, im guessing its intended to be a form of gambling, or pool hopping. Where you purchase 100,000 shares, then the public 100-200ghash, or whatever the speed is that day, get pointed at your pool until those shares get found.
I imagine that there is a possibility to make a lot of money that way, but from what I've seen in the GPUMAX forum, the odds of return are small. It just doesn't seem like enough to sustain the site, but I haven't purchased any shares either, so i'm not speaking from experience.
The reason you do it, is somewhat gambling. You purchase the shares for the extra horsepower if you will, to try and get "lucky". If you have it pointed towards a proportional pool, which pays out due to hash rate/shares used to solve the block, and you get lucky and get a block that is 1)Solved quickly, and 2) Multiple blocks solved within the time it takes you to get your shares, you can walk away with much more coin than what you put it. So if you buy 250k shares, and you get up to 600GH for it, you point it towards a proportional pool, and say it takes 500k to solve that block, and of that 500k, you grab 25k of those shares, you get a decent pay out because its proportional, not PPS. Now say you get really lucky and that takes only 10 minutes, well you have more shares coming your way so its on to the next block the pool finds. And again you are lucky and get somewhat the same result. When its all said and done, you can come away with much more than you put it. But again, its all about luck.
Where you get screwed like in this example, is when you dont get multiple blocks solved quickly. You get stuck in one of those 10 hour long rounds. Now, you are spending more coin than what you are getting. Its all about timing and luck.