The structures or patterns we are looking for are constraints, relations and dependencies within the data which are not obvious from the wide database-structure.
Additional structures can help us understand some connections in the database; in the extreme case it can lead to the elimination of redundant data-entries. The most important reason for finding structure is predictability: for example, if some of the data is known over some fields, then what are the probability or possibility-measures for other fields; an owner of a business may want to predict the buying behavior of his customers; some companies may want to predict fraudulent behavior of customers; a sociologist tries to predict group-dynamic behavior in specific social groups and to find out what role-behavior has the most influence to it; etc.