Shooting into the Sun - Image alert!

The short answer is that the surface of the sun is not solid; you're looking through the upper layers into deeper parts of the sun. The temperature, and hence brightness, increases the deeper you go, which is why the centre of the disc appears brighter and the limbs (peripheries) appear dark (or more accurately; you're seeing light emitted from deeper parts of the sun at the centre).

It's more or less the same process that explains why you're more likely to get sunburned when the sun's overhead at the equator; there's less of the Earth's atmosphere for the sun's light to travel through, so it can reach further before attenuating.

If you want to know more, the phenomenon is called limb darkening, and there's a fairly technical article here: http://en.wikipedia.org/wiki/Limb_darkening

I knew that astrophysics degree would come in handy for something