Domain services are Windows Communication Foundation (WCF) services that encapsulate the business logic of a WCF RIA Services application. A domain service exposes a set of related operations in the form of a service layer. When you define a domain service, you specify the data operations that are permitted through the domain service.
When designing a domain service, you should think of the domain service as a set of related tasks that you expect users to perform in your application. Typically, such tasks involve a small group of closely-related entities. For example, in an expense reporting application, you might expose entities for expense reports, line items, and details. You might, then, place entities for accounts and payments in a separate domain service[1].
Data Operations
You may add different data methods to a domain service that you want to expose like Query, Insert, Update, Delete. Besides these methods, you can also add more complicated operations, Invoke, Named Update. Named Update is to implement custom operations that do not fall into simple modification operations.
Convention
If you want to write a simple update method for ,lets say, Activity Entity, expected signature values should be as "public void UpdateActivity(Activity activity)".
It has to be like this for simple update operation for the Activity Entity. On the other hand, you can create an update method with different signature but some attribute has to be added to name of the update method. In that case, you dont have to follow the above convention. You can name your method as whatever you want. In below example, UsingCustomMethod attribute is set to true and as you noticed the name of the method is different.
And you can call this method in the code as follows;

So UsingCustomMethod attribute will give you the option to write more complicated operations.
References