Two important aspects of building your support workflow are collecting and processing your incoming tickets. You want to make it easy for your customers to contact you, but you also need an easy way to sort through all the various requests.
Now, with multiple support addresses in place, you can process incoming email based on which email address it was sent to. Instead of having one big, cluttered email inbox, your Zendesk can determine which email address the request was sent to and act upon it.
Suppose you run an online clothing store and you need to handle returns from customers. Instead of having those customers send return requests to your general support email, for you to then pass along to your Returns Department, you can set up an email address called firstname.lastname@example.org and set up a businness rule to automatically route return tickets to your Returns Department. That's collecting and processing in one step.