Indexing is a technique for improving database performance. The many types of index share the common property that they eliminate the need to examine every entry when running a query. In large databases, this can reduce query time/cost by orders of magnitude. The simplest form of index is a sorted list of values that can be searched using a binary search with an adjacent reference to the location of the entry, analogous to the index in the back of a book. The same data can have multiple indexes (an employee database could be indexed by last name and hire date.)
Indexes affect performance, but not results. Database designers can add or remove indexes without changing application logic, reducing maintenance costs as the database grows and database usage evolves.
Given a particular query, the DBMS' query optimizer is responsible for devising the most efficient strategy for finding matching data. The optimizer decides which index or indexes to use, how to combine data from different parts of the database, how to provide data in the order requested, etc.
Indexes can speed up data access, but they consume space in the database, and must be updated each time the data are altered. Indexes therefore can speed data access but slow data maintenance. These two properties determine whether a given index is worth the cost.