How does MySQL CASE work?

I know that SQL's CASE syntax is as follows:

CASE
    WHEN search_condition THEN statement_list
    [WHEN search_condition THEN statement_list] ...
    [ELSE statement_list]
END CASE

However, I don't understand how this works, possibly because I'm thinking about it as about an if statement.

If I have a field in table user_role, for example, which contains names like "Manager", "Part Time" etc., how do I generate a field role_order with a different number depending on the role. In the case of this example, "if user_role = 'Manager' then role_order = 5".

Please note I am looking for a teach a man how to fish answer rather than give a man a fish answer.