(CONVERTED AND EXPANDED BRETT LEHRER'S COMMENT)

I could be mistaken but I believe the purpose of that is to find all child ids for that parent without a recursive search. I don't know how that would work in the other direction, finding all parents from the child (without recursion).

parent_left and parent_right are special fields that are related to the parent_id field. The purpose of those fields is to make queries within the hierarchy execute efficiently: with parent_left and parent_right, you can retrieve all the descendants of a node without making recursive queries.

Consider two nodes A and B in the hierarchy. A and B can be partner categories, for instance. Their integer fields parent_left and parent_right are such that:

        B is a descendant of A in the hierarchy (defined by parent_id)

if and only if

        A.parent_left < B.parent_left, B.parent_right and B.parent_left, B.parent_right < A.parent_right

So, imagine that you have six partner categories like below. You can assign parent_left and parent_right by traversing the tree. The result is show in parentheses next to each node. Note that the values there are optimal; in practice, you can leave gaps in the numbers.
 - Customers (1, 10)
     - Consumers (2, 3)
     - Partners (4, 9)
        - Basic Partners (5, 6)
        - Gold Partners (7, 8)
 - Suppliers (11, 12)

You can retrieve all the subcategories of Customers with a single SQL query. Note that the values 1 and 10 are the parent_left and parent_right of Customers; they can be retrieved as part of the query itself.

        SELECT id FROM partner_category
        WHERE parent_left > 1 AND parent_left < 10

The last remark is that parent_left and parent_right can be updated without traversing the whole hierarchy. Removing a node does not require any change. For adding a node, you can adapt the parent_left and parent_right with two UPDATE queries: one to "make some space" between the parent_left and parent_right of the node's ascendants, and one to shift the parent_left and parent_right of all the nodes "at the right" of the new position. So parent_left and parent_right can be maintained efficiently.

More info: https://answers.launchpad.net/openobject-server/+question/186704