GAE still runs (virtual?) servers to handle HTTP requests. A server instance may start up, handle a number of requests, and shut down. At any given moment, a large number of server instances may all be running. Two sequential HTTP requests may end up being served by the same server instance or separate server instances. You need to design your software to be stateless, because you have no idea which server instance it runs on.
However, since GAE still runs virtual servers, it's possible that you can set some sort of global static variable that can be modified and accessed between multiple HTTP requests on a given server instance. Most likely you've done something along the lines of this.
This state is generally useless, because, as mentioned, you have no guarantees that subsequent HTTP requests will hit the same server instance, or any control on when a server instance is shut down. However, for example, if you wanted to run an experiment on how many requests each server instance serves on average, you probably could do that.