What the number means
Move your mouse one inch at 800 DPI and the sensor reports 800 counts. The game multiplies those counts by your in-game sensitivity to decide how far you turn. DPI is set in your mouse software or with a button on the mouse; sensitivity is set in the game. Neither number means much by itself.
The pair of them gives eDPI, and what your hand actually feels is cm/360: the distance you move to turn all the way around. Two players on wildly different DPI can have identical aim.
Why the number on the box is marketing
Gaming mice advertise 16,000 DPI, 26,000 DPI, higher every year. Almost nobody who aims seriously runs anywhere near those values. The overwhelming majority of FPS players sit between 400 and 1600 DPI and set the in-game sensitivity to produce the speed they want.
Cranking DPI and dropping sensitivity to compensate lands you in exactly the same place, with the added annoyance that your desktop cursor becomes unusable. The sensor in any current gaming mouse is flawless across the range you will actually use.
What to set it to
400 and 1600 are equally fine. Pick one, rebuild your in-game sensitivity around it, then stop thinking about it. The one real argument for 800 or 1600 over 400 is that the sensor reports finer increments, so very slow micro-adjustments are marginally smoother. It is a subtle effect, and plenty of top players still use 400.
The setting that genuinely ruins aim is not DPI, it is Windows pointer acceleration. Our mouse settings guide covers what to turn off, and raw input explains how games bypass it.
Changing it without changing your aim
If you switch DPI, scale your in-game sensitivity by the inverse to keep the same turn: going from 400 to 800 DPI means halving your sens. The eDPI calculator does the arithmetic and shows the cm/360 you end up with, so you can confirm nothing moved.