The purpose of a database index is to enhance the speed of data retrieval operations on a database. Similar to an index in a book, a database index allows the database management system (DBMS) to find records more efficiently without scanning every row in a table. Indexes optimize query performance by providing a structured way to access data based on specific fields or columns. While they improve read performance, it's important to consider that indexes can also incur overhead in terms of disk space and can slightly hinder write operations due to the need for updates.