The FOREIGN KEY constraint establishes a relationship between two tables by linking a column or a set of columns in one table (the child table or dependent table) to a primary key or unique key in another table (the parent table or referenced table). In the example from the presentation, the DEPARTMENT_ID in the EMPLOYEES table is defined as a foreign key. This foreign key references the DEPARTMENT_ID column in the DEPARTMENTS table. A foreign key value must match a value in the parent table or be NULL. The foreign key operates logically based on data values, and it is not a physical pointer, ensuring referential integrity between related tables. Additionally, an INSERT INTO operation may not allow foreign key values that do not exist in the referenced table, maintaining consistency across the database.