Consider a database table that is storing a category and a subcategory for a series of data. In this case, you don't expect to ever specify a subcategory without also providing a category. This is the sort of situation where a multicolumn index can be useful. B-tree indexes can have to up 32 columns they index, and anytime there's a natural parent/child relationship in your data this form of index might be appropriate.
Create an index for that sort of situation:
CREATE INDEX i_category ON t (category,subcategory);
The index could be used for queries that look like the following:
SELECT * FROM t WHERE category='x' and subcategory='y'; SELECT * FROM t WHERE category='x';
But it is unlikely to be useful for the following ...