DPI stands for dots per inch. Imagine your computer screen is a bunch of dots or pixels. DPI is how many dots your mouse will traverse per inch you move it. The lower the DPI the less your mouse will move. Low DPI means you will have much more precise aiming due to your mouse moving across less dots.
Auto recoil compensation is tricky. Basically it's when your cursor auto corrects itself after you fire a gun with recoil. When you turn this feature "off" it allows you to move your mouse and stop the recoil compensation from happening. And when it's on, the recoil compensation happens no matter what. I want to make a video on it because it's a lot easier to show than explain.