The apps are downloaded and your files remain local. It needs to check-in one in a while to ensure the license is still valid. Their servers went down for a day or two a while back. People's apps still worked, but they lost the ability to use the Adobe Font stuff... that wanted to be able to check the license either on each use, or far too often. They may have fixed that, as it was a lot of bad press at the time. So, barring any extended outage of internet, you should be fine. The CC apps can be activated on two machines, just like the old apps. I'm pretty sure you can mix and match PC/Mac just like the old apps too.

Old apps needed you to deactivate your license on the machine to get the license back, into order to install it elsewhere. That sucked if your machine died. Now that they require the occasional phone-home, they should be able to give you back a lost license, once the previous phone-home time limit has expired... Though I'm not sure they offer that. This question was what put me off getting the Photography CC subscription when it was announced, as I'd just lost a PC and one of my Elements licenses. I only decided to switch to CC when I got the 7D2, since a new Elements or Lightroom would be the same price, except I'd have full Photoshop. I still only went for it after I realized that even if Adobe don't offer any way to get your licenses back, I could cancel at the end of a year and buy it again with a new email address to get 2 new licenses... so it's not the end of the world.