Service design is the practice of designing products and services that are fit for purpose and use, and that it can be delivered by the organization and its ecosystem. There's a couple of key terms in the definition that we might recognize if you have read our ITIL 4 articles here at itil.diontraining.com.
First, fit for purpose. Fit for purpose is utility. It means making make that your products have good utility. They do what you need them to do. The next key term is fit for use in the service design definition. Fit for use is warranty. It is making sure that the product or service meets all of the standards and requirements that were given as part of your warranty. And then finally - delivered by the organization and its ecosystem. It is saying that you have the capability of doing it.
Take for instance Dion Training, a training company. They have a lot of capabilities that they can do but should they be doing video hosting? It is probably not one of their core capabilities so instead, they're not going to design that service in-house but instead design it and outsource that part of their brand. That way, even if it is not one of their core capabilities, they can still make sure they have a service that is fit for use, fit for purpose, and it can be delivered effectively by their ecosystem of partners and suppliers.
In service design, you want to think about your products and services and how you can best build them and design them, so that you're getting the best warranty and utility, for your organization.