A Generalized Search Tree (GiST) provide a way to build a balanced tree structure for storing data, such as the built-in B-tree, just by defining how keys are to be treated. This allows using the index to quickly answer questions that go beyond the usual equality and range comparisons handled by a B-tree.
For example, the geometric data types that are included in PostgreSQL include operators to allow an index to sort by the distance between items and whether they intersect.
GiST can also be used for full-text search, and it too has a very rich library of contrib modules that use its features. When you need a really customized type of index, with operators that go beyond the normal comparison ones, but the structure is still like a tree, ...
