Q: Why does the Eyedropper Tool set the Background color instead of the Foreground color when I click in my image?
A: The reason for this is that the Background swatch is "targeted" to accept the color information passed on by the Eyedropper Tool when you use it to sample a color. You can reset the behavior by clicking on the Foreground swatch in your Colors Palette/Panel. See the image below:
No matter which swatch is targeted, you can choose to temporarily sample color into the other swatch by holding down the Option key (ALT on Windows) while you sample with the Eyedropper Tool.
If you'd like to have the current Foreground and Background colors (as displayed in your Toolbox) switch places, simply tap the 'X' key on your keyboard.
Finally, to reset the Foreground and Background swatches to their default of black and white, simply tap the 'D' key.