These are concise and clear definitions from the Practical Service Design team.

Services are basically like a great concert. As someone who attends a concert, you see what happens onstage and are pretty happy about this experience. In a concert, it’s what happens on the stage that matters. You don’t really care how many cables and other machines and people are used backstage to make the concert happen. It's the same for a service, as a user, you only care about its frontstage. But it’s the backstage that makes it possible for the service to exist.

The backstage of a service is composed of all processes and tools used by the staff. When you use the services provided by your internet provider, you don’t see all the fancy servers and computers and cables that make it possible for you to see the funny cat videos on YouTube. That’s the backstage.

Today, there are many services that try to make the backstage of their service visible. This happens when you go to Domino’s for pizza and see the staff preparing your meal. By making the backstage visible in the frontstage it helps customers understand why it takes a few minutes to make a pizza.

So, the art of service design, is to decide what needs to be visible for the customer and what should stay hidden.