Higher mouse DPI allows you to move faster on the screen with less mouse movement. Higher resolution displays may require higher sensitivity or higher mouse DPI to attain the same amount of on-screen movement, or one would need a ridiculously large mouse-pad.
If you think about 1080p, to move 600dpi takes about 2 inches. 1200dpi will mean you'd only have to move the mouse @ 1 inch. So if you moved the mouse the full 2 inches, you'd cover twice as much distance on screen. With 1440p, the picture is smaller, expanded to fill the screen size, so you'd need to move the mouse 3 inches to cover 600dpi. So you'd raise dpi to lower actual space moved by your hand.
You'll have to do it in moderation, find what's comfortable for you. Most cheap mouses are 1600dpi and roughly move the same speed onscreen as you are moving your hand. Bumping dpi to high needs getting used to as the pointer ends up flying across the screen and you can't hit the broad side of a barn. Too low, and you won't hit anything but the barn without massive armswings.