Queues are a wonderful way of separating different parts of a system. Once you have separated those parts you can do lots of interesting things, like be more fault tolerant or have a more responsive front end for your users.

For example, lets suppose that we have a website on which we can book a holiday. We can choose lots of different options and at the end of the process when we've booked the holiday we'd like to send the customer a nice PDF detailing all the options they've chosen.