Quicker execution on the destination that YOU choose...instead of going to a middleman's desk and being shopped around.
You should go to some of the sites on this board and you can download a simulator that will show you the direct acess systems at work.....but be careful...one you go direct you will never go back..
Direct access is useful if your broker's auto-routing algorithm sucks. I stick with my current broker because of the platform, but with some stocks, my order isn't posted for around 15 to 30 seconds, and often the stock has moved through my bid or offer at that point. And my broker rarely sends a NYSE order to the NYSE - they send it to BSE or CSE, where it's typically the last to get filled. Even orders that arrive after mine, at the same price, get filled before mine.