DPI is how many pixels do you "travel" in a inch.
It is related to sensitivity but not at the same time. Having a higher DPI instead of more sensitivity is better and more precise as it's related to the mouse, not to the input. 800 DPI means that you would travel 800 pixels in a straight line if you move your mouse one inch. 2000 DPI 2000 pixels if you move one inch.
In games, if you have a smaller sensitivity but a high DPI on mouse, then you get better precision.
If you have mouse DPI settings, play a game with game-sensitivity-setting lowest and a big DPI setting on the mouse, then do the vice-versa. In my opinion the difference is quite noticeable.
I do not argue that anything over 3000 DPI IS pointless though. It means that in a inch you would travel a 1080p screen and a half in a inch. However, on lower mouse-sensitivity, it does help.
But there's a limit to how low you can set a game/mouse sensitivity to, so DPI still becomes obsolete as it may work faster than you'd want it to at a point or another, regardless of sensitivity.
Also I have
http://www.newegg.com/Product/Product.aspx?Item=N82E16826501010 for less than $20 with 2500 DPI (which is considerably perfect) and looks like a good copy for a gaming mouse.
