My personal step-by-step definition
What's a Service?
A service is an interaction between you and an organisation. This interaction should, in the end, bring you some value.
What's Design?
According to the contributors of Wikipedia, “design” connotes the following:
Design (as a verb: to design) is the intentional creation of a plan or specification for the construction of an object or system or for the implementation of an activity or process.
So what the fuck is Service Design?
So, Service Design is essentially the art of planning or creating interactions between humans and organisations.
I often translate this definition in layman's terms as the following:
Service Design helps organisations understand why people are so pissed about them and then fixes the problem.
Recommended resource
For more details about this question, I'd recommend you check out my free course called What is Service Design? Especially the section called "What is Service Design?"
Additional resources
In the little book called What the fuck is Service Design? I've collected answers to that question from Service Design practitioners from all around the world.
Marc Fonteijn wrote a short article called "What Is Service Design: The Final Answer" with a few interesting definitions.