Sunspots, such as this one, appear dark:
Sunspots are cooler because their magnetic fields inhibit the replenishing of heat from convective flows (due to the interaction between plasma and magnetic fields). This allows them to cool radiatively. The rest of the solar surface is constantly being replenished by convective cells that re-heat it.
Solar plasma at the photosphere radiates roughly as a black-body, meaning that the energy (and wavelength) spectrum of radiation follows the Plank function. The Plank function scales up and down with temperature at all energies (and wavelengths). The brightness of a blackbody at a given energy (or wavelength) is determined by the value of the plank function at that energy.
The image you showed is taken in the 'photospheric continuum', which is a black-body dominated part of the radiation spectrum. So, because Sunspots are cool (compared to their surroundings), this means that their Plank function is lower than their surroundings, and hence their brightness is lower, causing them to appear dark in the image.
Typical sunspots have a dark region (umbra) surrounded by a lighter region, the penumbra. While sunspots have a temperature of about 6300 °F (3482.2 °C), the surface of the sun which surrounds it has a temperature of 10,000 °F (5537.8 °C).
From this NASA resource:
Sunspots are areas of intense magentic activity, as is apparent in this image:
You can see the material getting stretched into kind of getting stretched into strands.
As for the reason it is cooler than the rest of the surface:
All in all, the sunspots appear dark because the are darker than the surrounding surface. They're darker because they are cooler, and they're cooler because of the intense magnetic fields in them.