Indexes may also be used to enforce uniqueness of a column's value, or the uniqueness of the combined values of more than one column.
CREATE UNIQUE INDEX name ON table (column [, ...]);
Only B-tree indices can be declared unique.
When an index is declared unique, multiple table rows with equal indexed values will not be allowed. NULL values are not considered equal.
PostgreSQL automatically creates unique indices when a table is declared with a unique constraint or a primary key, on the columns that make up the primary key or unique columns (a multi-column index, if appropriate), to enforce that constraint. A unique index can be added to a table at any later time, to add a unique constraint. (But a primary key cannot be added after table creation.)
Read the upstream documentation. For corrections, first check the current manual.