An expression index is a database index that is built on a generic expression, rather than on a list of columns. This allows indexes to be defined for common query conditions that depend on data in a table, but are not actually stored in that table.
A common use for an expression index is to support case-insensitive searching or constraints. For example, if a web site wants to make user names case-insensitive, but still preserve the case as originally entered by the user, a unique index can be created on the upper- or lower-case representation of the user name:
CREATE UNIQUE INDEX site_user__user_name_lower ON site_user( lower( user_name ) );
That will create a unique index on "lower(user_name)". Any queries that search on "lower(user_name)" could then make use of that index:
SELECT user_id FROM site_user WHERE lower(user_name) = lower('Decibel');