The question is about Play framework specifically although concept is generic. I guess that the blocked client is listening to a socket which is tracked on the server side and passed around with the Future[Result] so that when the Future finishes, then the response is written to the socket and then the socket is closed.
Can someone share more concrete explanation with references?
Quoting from:
https://www.playframework.com/documentation/2.6.18/ScalaAsync
The web client will be blocked while waiting for the response, but nothing will be blocked on the server, and server resources can be used to serve other clients.
Note that Play does not manage how to address the client. This is managed by TCP. Basically (as a simple analogy) you can think of a client, like a web browser, as making a telephone call to the server. When the clients makes a request, one of it's sockets gets connected to a particular socket on the server - this is a persistent connection between the sockets for the duration of the request/response. Play's underlying server (Netty for older versions or Akka Http for v2.6+) will accept the incoming request from the socket and assign it a thread. Play will do the work and the resulting Response will get mapped back to the correct socket by the server. The TCP server will manage the mapping between response and the socket, not Play.
As others have noted, the reference to blocking is essentially to do with the way Play Action's are intended to work (non-blocking). They take the request, wrap whatever work you have coded in a Future, and hand this off to get completed at some point in the near future (it might be a different thread that completes the Future, or it could even end up being the same thread). The point is that the creation of the Future is quick and so the thread that handled the request gets returned quickly to the pool so it can pick up another request to work on. If you have heard about Reactive Programming then this is essentially the idea being keeping an Application Responsive.
The web client will be blocked while waiting for the response, but nothing will be blocked on the server, and server resources can be used to serve other clients.
So the client might be blocked on it's end whilst waiting for the response to come back through it's socket (unless it too is making async calls), but the idea is that the thread pool handling the requests in Play will not be blocked because of the way they create a Future and hand the completion of this back to Play so they can go back to handle other requests.
There is a bit more to it but hopefully this gives a bit more context to that particular statement from Play's docs.