The strength of the relationship between two variables is usually the most important information that we gain from a scatterplot but a scatterplot may display other features.
Outliers
Values that seem 'different' from the rest of the data are called outliers.
An outlier may be an extreme value of one or other variable, but an individual may be an outlier even though neither X nor Y is unusual on its own. One point is an outlier in each of the three data sets below.
The point is an outlier in the righthand data set because it lies well above the main group of points — its y-value is much higher than others with similar x-values.
Importance of outliers
Outliers are features of a data set that must be carefully checked. An outlier is often caused by a recording or transcription error, so...
First check that the values of the variables are correctly recorded.
Sometimes an outlier arises because an individual is fundamentally different from the others. Identifying what makes the individual different often gives considerable insight into the data.
The individuals should be further examined (perhaps collecting further information from them) to try to assess whether the outlier individual has distinct characteristics.
An outlier that is either extreme or that has other distinctive characteristics would often be deleted from the data set, but should be mentioned in a report about the data.