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 one to many table. Such a table usually sits between two indexed tables, for example:

CREATE TABLE left (id INT PRIMARY KEY, ...);
CREATE TABLE right (id INT PRIMARY KEY, ...);
CREATE TABLE one_to_many(left INT REFERENCES left, right INT REFERENCES right);

It is typically used like this:

SELECT right.* from right JOIN one_to_many ON (right.id = one_to_many.right)
  WHERE one_to_many.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 one_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 left, int_array_aggregate(right) AS right
  FROM one_to_many
  GROUP BY 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 left, int_array_enum(right) FROM summary WHERE left = item;

The above query using int_array_enum produces the same results as

SELECT left, right FROM one_to_many WHERE 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 one_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 one_to_many table, which was replaced by:

SELECT right, count(right) FROM
  ( SELECT left, int_array_enum(right) AS right
    FROM summary JOIN (SELECT left FROM left_table WHERE left = item) AS lefts
         ON (summary.left = lefts.left)
  ) AS list
  GROUP BY right
  ORDER BY count DESC;