Item response theory is a modern approach to psychometrics that models how the probability of a specific answer relates to a person's underlying trait level, item by item.
Where classical test theory looks at a test's total score, item response theory zooms in on individual questions. For each item, it estimates things like how difficult the item is (how much of the trait someone needs to endorse it) and how well the item distinguishes between people at different trait levels. This lets researchers build much more precise and efficient tests — including adaptive tests that select each next question based on how you answered the last one, homing in on your trait level with far fewer items than a fixed-form test would need.
Item response theory is also what makes it possible to fairly compare scores from different test forms, since it accounts for the fact that not all versions or all items are equally difficult. This matters for large-scale testing programs where not everyone sees the exact same questions.
The tradeoff is complexity: item response theory requires much larger samples and more sophisticated statistics to develop than classical test theory, which is why plenty of well-built assessments still rely on the classical approach.