Discriminant analysis' primary object is most easily understood through example. For example, to predict the probability that someone will be included in a group of successful college graduates at your university, use the known observation set of SAT scores, high school grade point average, having an older sibling in college and class rank.
The secondary objective of discriminant analysis is to determine the quality of the variable used in your primary prediction. In our example, once time has passed and you can observe the group of successful college graduates, you can model your prediction theory against the actual outcome. You can determine which variables were best at predicting an individual's successful inclusion.
Retrospectively analyzing the predictive theory against actual results creates a third objective, improving the predictive model for the future. Using your analysis, you can show which variables were most relevant to success. In our example, we may determine that having an older sibling in college was a worthless predictive observation. We can decide to leave it out of our next prediction or include a different observation.