This graph shows the 11-year cycle from about 1700, but astronomers only start counting cycles from 1755. The first cycle peaked about 1760. You can see from the figure that the maximum number of sunspots changes a lot from each cycle to the next. This makes predicting what will happen next very difficult. Count the peaks in the figure to see how many complete sunspot cycles their have been. You should count 22. Which is the largest cycle? When roughly did it peak?
Since there have been 22 peaks, we must now be in Cycle 23 which started in 1996. This cycle is predicted to peak in the year 2000 at a sunspot number of at least 130.
The cycle isn't just about sunspots. It turns out that all kinds of things on the Sun (e.g. flares, prominences, coronal mass ejections) go through the same cycle and are most common when sunspots are most common. Thus we can talk about a general solar activity cycle and not just the sunspot cycle.
We don't know why yet, but we do know it has something to do with the Sun's magnetic field. At the peak of the cycle, the Sun's magnetic field is all twisted up and complicated. At the lowest point of the cycle, the magnetic field is much more simple. We also know that there are strong magnetic fields where sunspots are produced.