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 actually regions of the solar surface where the magnetic field of the Sun becomes concentrated over 1000-fold. Scientists do not yet know how this happens.
Why are sunspots dark? ... Because magnetic fields can produce pressure, inside sunspots, the gas does not need to exert quite as much pressure as elsewhere on the Sun to insure that the total pressure across a sunspot is in equilibrium with the gas surrounding the sunspot. Since the cooler a gas is, the less pressure it exerts, this means that ...
Sunspots appear dark (in visible light) because they are much cooler than the rest of the surface of the Sun. However, even though they appear dark, they are still very hot. Sunspots have temperatures around 6,300 Fahrenheit (~3,500 Celsius) while the surrounding surface of the sun has a temperature of about 10,000 Fahrenheit (5,500 Celsius).
Why do sunspots look darker than the rest of the sun's photosphere? ... Sunspots are temporary phenomena on the photosphere of the Sun that appear visibly as dark spots compared to surrounding regions. Prominence. a stream of incandescent gas projecting above the sun's chromosphere.
Sunspots are areas of gas on the sun's surface that are cooler than the gases around them. Cooler gases don't give off as much light as hotter gases, which is why sunspots look dark.
Sunspots are dark because they are much cooler than the surrounding portions of the sun, according to Cool Cosmos, a joint project by the National Aeronautic and Space Administration’s Jet Propulsion Laboratory and California Institute of Technology’s Infrared Processing and Analyses Center.
In regular photographs, sunspots appear dark because the temperature of surrounding areas is so high that by comparison, sunspots are cool. In reality, they are still immensely hot.
Sunspots look dark because they're 3,000 degrees Fahrenheit cooler than the surrounding photosphere. They are in fact much hotter than the arc generated by an electric arc-welder and a large sunspot by itself in the sky would outshine the full moon.
Any given appearance of a sunspot may last anywhere from a few days to a few months, though groups of sunspots and their active regions tend to last weeks or months, but all do eventually decay and disappear. Sunspots expand and contract as they move across the surface of the Sun, with diameters ranging from 16 km (10 mi) to 160,000 km (100,000 ...
Ok, both of the other answers so far are wrong. While there is still ongoing research into how sunspots form we know it has to do with the sun's magnetic field. They appear dark because the area around them is brighter than they are because sunspots have a lower temperature.