find my iPhone just showed a compass before, now it shows my phone as offline

My phone seems to have been taken. When I logged into find my iPhone before, all it would show me was a rotating compass wheel but it would never do anything else.

Today, it popped up and said my phone is offline.

Does this mean that someone had my phone turned off before and I got the rotating compass, but now they turned it on and it is showing as offline. Do I just need to wait and see if they go online with it?

I have checked Notify me when it goes online. Does this mean I will get an email to notify me?

I have left the window open that says it's Offline, if I leave that open, will it just notify me there on that window?

Thanks.