My understanding is that Amber puts your nsec onto your phone and then you can use that to log in to things like amethyst or other nostr clients. 

 That's how I've been using it 

 I recently discovered this. Under permissions you can create an "app" and you get an nsecbunker url that you can use once.

Once the website has connected, it will communicate with your Amber remotely.

You may need to enable internet for Amber as I had to on Graphene OS. Amber doesn't need internet to sign for Amethyst, but it does for remote signing.