Sun spots were known to the ancient Chinese who probably could see the largest spot groups when the sun's glare was filtered by dust from the various central Asian deserts.
They were first observed telescopically by a German astronomer [Johannes Fabricius]? in 1610: there was dispute between Christoph Schreiter and Galileo Galilei over priority of their discovery. Sunspot research remained dormant after this due to the [Maunder Minimum]?, during which no sunspots were visible for some years, but after the resumption of sunspot activity, Heinrich Schwabe in 1843 reported a periodic change in the number of sunspots.
Although the details of sunspot generation are still somewhat a matter of research, it is quite clear that sunspots are the visible counterparts of [magnetic flux tubes]? in the convective zone of the sun that get "wound up" by [differential rotation]?. If the stress on the flux tubes reaches a certain limit, they curl up quite like a rubber band and puncture the sun's surface. At the puncture points convection is inhibited, the energy flux from the sun's interior and with it the surface temperature decreases.
This model is supported by observations using the [Zeeman effect] that show that prototypical sunspots come in pairs with opposite magnetic polarity. From cycle to cycle, the polarities of leading and trailing (with respect to the solar rotation) sunspots change from north/south to south/north and back.
The sunspot itself can be divided into two parts :
Sunspots usually appear in groups, and their lifetime is about two weeks. The [Wilson effect]? tells us that sunspots are actually depressions on the sun's surface. There is a regular sunspot activity that begins in the higher latitudes and moves toward the equator. Sunspot activity cycles about every ten years (7.5 - 11). This is called the [Spoerer law]?. The point of highest sunspot activity during this cycle is known as Solar Maximum (Solar Max for short), and the point of lowest activity is Solar Minimum (Solar Min).
Today it is known that there are various periods in the [Sunspot Index]?, the most prominent of which is at about 11 years in the mean. This period is also observed in most other expressions of [solar activity]? and is deeply linked to a variation in the solar magnetic field that changes polarity with this period, too.
Sunspots are relatively easily observed -- a small telescope with a projection facility suffices. Note: Never look directly into the sun; Galileo's eyes did not survive this, and yours will not either.
Due to their link to other kinds of solar activity, they can be used to predict the [space weather]? and with it the state of the ionosphere. Thus they can help predict conditions of short-wave propagation or satellite communications.