When light hits the sensor it creates a spot the same shape as the aperture but at size dependant on real world distance of the source object from the plane of focus. If the aperture is a circle you get a circle, if the aperture is square you get a square. The bigger the aperture, the bigger the shape, thus it will overlap more with neighbouring shapes and give you more blur.

As you get close to the focal plane the size of the shape projected into the sensor is so small it's indistinguishable from a dot. These distances define the depth if field.
 
Your eye works in exactly the same way, but I wouldn't trust what you're seeing as the brain does a crazy amount of processing!