think of blackberry as a little mini-internet
the service providers (ie vodaphone, o2, orange etc.) have their own connections into this network.
your blackberry device will connect to the blackberry mini-internet via a local accesspoint provided by your service provider. this should be either free or very low cost depending on your data package. you will have an always on connection to this network.
your blackbeery will talk to the main blackberry mail servers to send/receive email (it's push email, so itll go straight to the handheld)
your BES will be connected to the internet, and havea connection open to the blackberry mail servers. this is how is passes information between your exhange (or notes) server and the device (ie youre using a 3rd party)
its just a very over-complicated internet mail system really.
and PUSH email, isnt really push, since the device is always talking to the blackberry servers, its not like it magically establishes a connection that wasnt there before