The aggregator is an aggregate function int_array_aggregate(integer) that produces an integer array containing exactly the integers it is fed. This is a wrapper around array_agg, which does the same thing for any array type.

The enumerator is a function int_array_enum(integer[]) that returns setof integer. It is essentially the reverse operation of the aggregator: given an array of integers, expand it into a set of rows. This is a wrapper around unnest, which does the same thing for any array type.

Many database systems have the notion of a many to many table. Such a table usually sits between two indexed tables, for example:

CREATE TABLE left_table  (id INT PRIMARY KEY, ...);
CREATE TABLE right_table (id INT PRIMARY KEY, ...);
CREATE TABLE many_to_many(id_left  INT REFERENCES left_table,
                          id_right INT REFERENCES right_table);

It is typically used like this:

SELECT right_table.*
FROM right_table JOIN many_to_many ON (right_table.id = many_to_many.id_right)
WHERE many_to_many.id_left = item;

This will return all the items in the right hand table for an entry in the left hand table. This is a very common construct in SQL.

Now, this methodology can be cumbersome with a very large number of entries in the many_to_many table. Often, a join like this would result in an index scan and a fetch for each right hand entry in the table for a particular left hand entry. If you have a very dynamic system, there is not much you can do. However, if you have some data which is fairly static, you can create a summary table with the aggregator.

CREATE TABLE summary AS
  SELECT id_left, int_array_aggregate(id_right) AS rights
  FROM many_to_many
  GROUP BY id_left;

This will create a table with one row per left item, and an array of right items. Now this is pretty useless without some way of using the array; that's why there is an array enumerator. You can do

SELECT id_left, int_array_enum(rights) FROM summary WHERE id_left = item;

The above query using int_array_enum produces the same results as

SELECT id_left, id_right FROM many_to_many WHERE id_left = item;

The difference is that the query against the summary table has to get only one row from the table, whereas the direct query against many_to_many must index scan and fetch a row for each entry.

On one system, an EXPLAIN showed a query with a cost of 8488 was reduced to a cost of 329. The original query was a join involving the many_to_many table, which was replaced by:

SELECT id_right, count(id_right) FROM
  ( SELECT id_left, int_array_enum(rights) AS id_right
    FROM summary
    JOIN (SELECT id FROM left_table
          WHERE id = item) AS lefts
    ON (summary.id_left = lefts.id)
  ) AS list
  GROUP BY id_right
  ORDER BY count DESC;