PostgreSQL allows partial indexes, where only rows that match a predicate are indexed. For instance, you might want to index the customer table for only those records which are active. This might look something like:
create index i on customers (id, name, whatever) where is_active is true;
If your index many columns, and you have many inactive customers, this can be a big win in terms of space (the index will be stored in fewer disk pages) and thus performance. To hit the index you need to, at a minimum, specify the predicate:
select name from customers where is_active is true;