How to structure a model to properly and efficiently represent tree-like data on relational databases?
I believe he is going for something like a binary tree.  I would just include three keys that are tied to the unique id of the same table, one for the left, one for the right child, and one for the parent.

i.e.- (very much pseudocode)

TABLE tree
int         id                  autoinc
varchar(16) data_you_care_about
int         parent_id
int         left_child_id
int         right_child_id

FOREIGN KEY parent_id = tree.id
FOREIGN KEY left_child_id = tree.id
FOREIGN KEY right_child_id = tree.id