I know the answer to this conundrum, but I still have problems recognizing the answer. If you’ve never seen it before, it is really baffling.
Which is the true statement about the image below?
(Click to enlarge to full size. It might help.)
The illusion was invented by Edward H Adelson in 1995. The best way to work out the solution empirically rather than by sight is either to import the full image into Photoshop (or whatever tool you use for image processing) and use its eyedropper tool to find the RGB values, or to print it out and then cut out the two squares to compare them directly.
If you want to explore this illusion more, I would go to the source: Adelson’s pages about it.