adasiek correct.
Pusher send request to the client. So instead of having the client checking the server continuously it's the server that send output whenever there is something new (keeps one stable connection open with the server).
The decision of implementing this simple service with pusher,I believe, was only for there simple framework and good documentation. It is very expensive (smallest monthly fee is 50$) but is easly simulated (you can configure a server to act exactly like pusher, but do need some minimun IT skills).