As a child, one of the first things you learn is how to recognize shapes. You might have a toy like this where you put different shaped blocks into the right hole. Then, later, you learn these shapes have names.
The illusion is known as the Coffer Illusion, due to its resemblance to the coffers (sunken panels) on wooden doors. It was created by Dr. Anthony Norcia at The Infant Vision Laboratory at Smith-Kettlewell.
If you counted more than 16 circles, there's a good chance you were looking at the areas indicated by the red circle seen here. There does appear to almost be circles horizontally in between the rectangle rows, but not quite. The lines don't quite go all the way around, so there are only 16 circles total, not 25.
Now that you're aware of the circles, you probably can't look at the image without the circles sticking out like a sore thumb. Maybe you'll start seeing circles everywhere, even if none are present. Solving illusions can be dangerous business.