Controller Activation Is Convenient
Whether the subject is the older XML Web Services (a.k.a. ASMX services), WCF, services with ASP.NET MVC or with the ASP.NET Web API, the concept of service activation is present.
Essentially, since by-and-large all calls to a service are new requests, the ASP.NET or WCF runtime activates a new instance of the service class for each request.
This is similar to object instantiation in OO-speak. Note that service activation is a little more involved than simply having the application code create a new object.
Understanding activation and dependency resolution is very important if you want to have a solid grasp of any service application, including the ASP.NET Web API.