Terminable middleware in Laravel works by first handling the incoming request in the handle method. This method passes the request to the next middleware or the application, which generates a response. After the response is sent to the client, the terminate method runs. This method is useful for tasks like logging or cleanup that should happen after the user receives the response. The terminate method cannot modify the response because it runs after sending. The execution flow starts with the request entering middleware, handle passing it on, response generation, response sending, then terminate running, and finally middleware finishing. Variables like request and response change state accordingly but remain accessible in terminate for post-response actions.