OK, so we've all heard this one before. However, it holds true: the Sun is like an onion, not just because it'll make you cry if you look at it for too long, but because it has layers, each of which differ distinctly from each other.
The core is the critical point of the star, where nuclear fusion takes place and generates all that heat and light. This is possible due to the gravitational pressure exerted by the rest of the star, keeping it compact and thus ripe for nuclear reactions, turning hydrogen into helium.
Moving outwards, the atmosphere gets progressively less dense, but no less tumultuous. Powerful currents move within the Sun, transfering the heat through the radiative zone into the convective zone. This process creates thermal columns of rising and sinking gas as it rises and cools then sink and heat up again.
The next layer out, the photosphere, is the visible layer of the Sun: we can't directly see all those previous layers due to the photosphere's opacity—which is where all our spiffy technology comes in handy. A lot we can figure out indirectly from the action on the photosphere and from observing at different wavelengths, but nonetheless, the deep parts of the Sun are less well understand than outer laters.
Everything above the photosphere is technically considered atmosphere, mostly consisting of the corona. Oddly enough, this is the hottest part of the Sun. Long plasma filaments twist and leap into the corona, and solar wind streams out in a radioactive breeze. This part of the atmosphere is like an eternal firestorm.
This part of the Sun is typically studied with the aid of a device called a coronograph, which basically just blocks out the light from the main part of the Sun, letting astronomers look only at the light of the corona, which is otherwise hard to see.