The Eyedropper tool is used to sample colors that are already on your canvas. It seems straightforward, but what happens when your layers are set to different blending modes? This video explains a bit more in-depth about the eye dropper tool, and how you might use it in a complex painting. It may seem like the Eyedropper is of only minor importance, but to a digital painter it becomes one of the most frequently accessed.
To learn more about the on-screen mixing talked about in the video, try these others:
Digital Painting 101 #3, Brush Control Basics , Blending Technique