It's a tool that you can use it to pick colors, an easier way of doing the same is to drag the color selector, but the picker will show you a more detailed result, and with customizable settings!
The picker auto-switches back to the last tool you used.
The picker may pick colors only on the current layer, or the one above, the ones below, or all layers! The difference between mixed and separated, is that if one layer has a semi-transparent color, the mixed mode will mix it with the colors below it before passing it to the picker, where the separated mode will get the color as is.
If set to No, will ignore alpha completely, otherwise, will set the opacity while picking.