What exactly does "moving the market" means? Means that these dark trades won't affect the price of the BTC?
They will ultimately affect the price of the BTC through demand/supply rules. But there will significantly less immediate effect on the market comparing to normal, visible order, so this helps to combat short-term volatility.
Please check depth of market and megachart on mtgox to see what we're talking about (
http://mtgox.com/trade/history).
Now to see how it works, consider that you want to buy a lot of USD for BTC. Let's say 5000 BTC which is more or comparable to sum of current bids.
If you'll try to buy it at market price going through current bids starting from highest you will fill a lot of bids and thus drive the highest bid down. So it is not a very good idea. Even you do this gradually, still highest bid will decrease over time from your activity, people will notice this and will put both their bids and asks lower, thus you're losing again.
If you do not want to buy at a huge premium you can try to buy at fixed price. Let's say lowest current ask is 0.79. Then you can put your ask at 0.78. Then, in theory, people who sell at market price will eventually fill your order without driving price down.
But the problem is that others see your ask order and its size and they will anticipate drop in price of BTC through demand/supply balance. Besides that there are other people who want to buy and they will try to put their asks lower than yours, e.g. 0.7799 < 0.78 to get their orders filled before yours by market orders. (As there is no chance that anybody can buy at better price in near future.)
Thus again, price is going down and you're not buying anything until some huge-ass sell order will appear.
Dark orders are kind of solution to this problem -- you're still buying something but people do not see your orders so they cannot anticipate whether market goes up/down before you do.
In dark+normal situation it is like a normal order but it is invisible. People will see that something happens -- ask orders are not filled at market, or are not filled as fast as they should, but they will not know what is your price and how much volume is left. So they cannot anticipate drop in price and drop it before that.
With dark-only situation you'll be trading among other dark-poolers (people with huge orders). So it will be invisible to normal market, but affect it because there are less volume flowing through it. Dark-poolers will probably use current market price as a reference for their orders.
So this stuff is unnecessary if there is huge volume in trading and so individual orders do not move market much. But it looks like it is not a case with bitcoin exchanges so far because there are different players with different capacities.