A uniqueness constraint ensures that all values in a column are different from one another. This is crucial to prevent duplicate entries that can lead to inconsistencies in the database. For example, if the uniqueness constraint is applied to a customer email column, it guarantees that each email address is only entered once, thus maintaining the uniqueness of the customer records. The other options are incorrect because a relational constraint does not ensure uniqueness, a primary key is a specific type of uniqueness constraint but does not describe its purpose, and the foreign key constraint is associated with linking tables together, not ensuring uniqueness.