The classic use is removing slow operations from a user-facing path. Sending an email, generating a report or processing an upload does not need to block an HTTP response — the request enqueues the work and returns immediately, while a worker handles it independently.
Queues also provide backpressure. When consumers cannot keep up, the queue grows rather than the system failing, giving time to scale workers up. The design requirement this introduces is idempotency: a message may be delivered more than once after a failure, so processing it twice must be harmless. Systems that assume exactly-once delivery break in production.