Read all about it here:
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dpi talks about the amount of times the mouse transmits it's co-ordinates per inch of movement. There is also a measurement of the amount of shot per second which measures the reaction time of the mouse (how well it performs if you move the mouse quickly). For example, the MS Intellimouse explorer runs at 6000 shots per second and 400 dpi. The Logitech dual mouseman optical (the 2X optical) runs at 2000 shots per second and 800 dpi. If you read all the sales stuff, it means that the Dual Mouseman can be moved with more precision and the Explorer reacts quicker to movement.
The Logitech Dual Mouseman has 2 optical sensors in it instead of just one. The idea is that whichever sensor has the best idea of what's going on, that's the sensor the mouse uses. It's meant to work better on a wider variety of surfaces (wierd mouse mats for example). I've used both mice, and although the logitech one can be adjusted so that less movement moves the pointer further across the screen than the MS one, when you adjust both to acceptable use levels, I can't notice much of a difference. I like the feel of both, but I use the MS explorer 3 because it has the extra button (it has 5 buttons including the wheel whereas the Dual Maouseman only has 4).