Higher DPI settings allow you to move faster on the screen with less mouse movement, or increase precision by using reduced sensitivity in conjunction with higher DPI.
Higher resolution displays require higher sensitivity or higher DPI to attain the same amount of on-screen movement, and higher sensitivity settings with a low DPI mouse can limit precision. This is manifested by movements occurring in increments of more than one pixel, making it difficult to precisely aim or otherwise make fine movements. Higher DPI allows you to increase movement speed without increasing the sensitivity setting, giving you more precise control.
Note that this really isn't that big a deal with a lower resolution display. I use a ROCCAT Kone XTD, and I have the mouse set to 1800 DPI with sensitivity at -2 (on a scale of -5 to +5). This is on a run-of-the-mill HP laptop with a 1366x768 display, so DPI settings much higher than this (up to 8200 DPI) are essentially unusable for me. Higher DPI will definitely make a difference on larger displays, though.