A sunspot is defined as a cooler darker spot appearing periodically on the sun's photosphere; associated with a strong magnetic field. Sunspots have been appearing on the sun for as long as astronomers can remember however; it wasn't until late 2002 when the most detailed image of the sun showed that sunspots do in fact have an internal structure (leading to a greater understanding of these mysterious blotches).
The images taken on the one-meter solar telescope at the Royal Swedish Academy of Science's Observatory has taken a picture with high enough resolution to reveal the structure of the smaller circle of the filaments. This technology was brought about after other scientists noticed that the sunspots were more than skin dip after analyzing sound waves ricocheting inside the sun, revealing fast-moving streams of hot plasma penetrating below the solar surface.
So this has brought about the findings of the sunspots structure which include the following:
The dark areas on the surface of the sun are called UMBRA (the magnetic field is approximately vertical) and are surrounded by the PENUMBRA (the brighter regions of the filaments which are difficult to understand, being made up of complex magnetic-field geometry, interacting with gas flows and oscillations). Below the surface of these sunspots the temperature is actually hotter than most other parts of the sun, coinciding with the much cooler sunspots themselves averaging around 4000 - 5000 degrees Fahrenheit. The structure of sunspot penumbrae can be easily defined in terms of bright filaments on a dark background, as opposed to dark filaments above a bright granular background.
In the convection zone of the sun, that gets wound up by the differential rotation, the magnetic flux tubes get stressed, forming it to curl up (similar to rubber bands) and then puncture the surface of the sun causing the array of flares similar to certain hurricanes as they are self-perpetuating storms.
Sunspots are still very much a mystery to scientists, physicists and the general population. They can last from a few weeks to only a few minutes because the magnetic field lines ordinarily repel each other. They vary in height, as some can be visible with the naked eye (of course if appropriate eyewear is worn) while some are only slightly visible with the help of a telescope.
The two main parts (the UMBRA and PENUMBRA) are still being researched to find out greater detail to the sunspots structure!