Here's the puzzle:
The two marked squares ARE the same color, in spite of what your eyes are telling you.
Here I've lined all of the main shapes to maintain the feel of the original image and in preparation for removing all other color and tone from the image.
And here it is with the two colored squares isolated. I've done absolutely nothing to the color of the squares to make them the same. They always were the same. All I did is remove the colors that were influencing how your eye was perceiving them. Try it yourself with the original image if you don't believe me.
This is something that I originally learned of around 12 years ago when I was spending way too much money to commute to Denver for Art School. A similar image was used by my Color Theory instructor to demonstrate one of the Seven Types of Color Contrast. In this case, I'm pretty sure it's Simultaneous Contrast.
You can read more about illusions and see this one as well at this Wikipedia page. There is also another example of Simultaneous Contrast there involving a solid gray bar resting on a grey gradient and taking on the appearance of being a gradient itself.
Also a LOT more info and cool stuff can be found here.
This is why I loved Color Theory. I'm such an art geek.
UPDATE: I googled the name on the picture and came up with this site. All the answers are here! I bet! 'Cause I didn't actually read it yet. But he has a page called "Explanation," so unless that's a lie... Um. Yeah.