Yeah, it works completely locally on the lan - there's a MDNS discovery and then pairing process between devices and the phone.

You can access stuff remotely if you have an Apple device which is paired to the homekit stuff and connected to the internet (e.g. an Apple TV, we use an iPad which is always at home).

I've deliberately designed my system to work offline as while our connection's pretty reliable I don't see why I should need an internet connection to turn on a light! :)