An important motivation for studying relations and relational algebra is that these formal concepts underly the organization and manipulation of data in databases. In fact, most databases are more accurately called relational databases precisely because the database is used to access relations.
In the relational data model, information is stored in tables (i.e., relations), where the columns are associated with attributes and the rows contain the values for each attribute.
Information can be added, deleted, or retrieved from a relation using a standard set of operations on relations, however the real power of relations comes about from operations that span relations.
An important use of the relational data model is in database design, where we must choose an appropriate collection of relations, and implement operations on those relations efficiently.
Database queries can be expressed as operations in a relational algebra, where algebraic laws of relational algebra are used to simplify queries, and thereby optimize the implementation of database operations.