When you describe something as exigent, you are saying it requires attention: it can't be ignored.
Exigent, which means "demanding attention," comes from the Latin for "driving out." If there's a runaway train driving straight at you, that's an exigent situation — not a good time to stop and write a poem. When circumstances become exigent, it's time to act. When exigent questions arise, an answer is necessary. You can also use exigent for a person who demands attention, usually by complaining. If you've ever worked as a waiter, you've surely dealt with an exigent customer.