A scatter chart shows clusters of information. Rather than displaying connections like line graphs and bar charts, a scatter chart just puts information points on the axis and lets users draw their own conclusions.
One key feature of a scatter chart is that it can correlate two sets of data. For example, you could make a scatter chart of days of the week and number of sick days taken by your staff; the days of the week would be on one axis and the number of sick days would be on the other. If your staff were taking more sick days on Mondays and Fridays than they were other days, this would be immediately obvious, as there would be two large groupings of dots at Monday and Friday. A scatter chart can correlate data that isn't necessarily linear.
Large Data Set
Scatter charts often are used for large data sets. The individual pieces of information are not as relevant in a scatter chart as the large-scale correlations between them. Even if you have thousands of pieces of data, you are only interested in how they group, not in how many are in each grouping. So, if you were comparing sick days taken to the days of the week for 20,000 employees, the result would look essentially the same as it would if you were doing so for a 100 employees. The difference would be that the concentrations would be thicker for the larger employee group.
A scatter chart can show immediately what "normal" behavior is for a set of data. It also can show the converse -- where the outliers are and how many there are. For the sick days graph, an HR manager would immediately know that most employees take sick days on Mondays and Fridays. However, if barely anybody takes a sick day on Tuesday or more people take sick days on Thursdays than Saturdays, the HR manager also would immediately be aware of this fact.
Single Data Set
A scatter chart's main strength is its ability to put large amounts of information in an instantly comprehensible, easy-to-understand format. It is possible to add more data to a scatter graph, in the form of different-colored points, but this is not usually recommended because multiple data sets just make the scatter graph confusing.