This basic assumption that the Internet will always be there is a faulty assumption. The Internet is best described as a graph of servers, each capable of talking to the others:

Network topology

A Server is anything that talks on the Internet: your laptop, your mobile phone, the machine hosting your Cloudant database, and so on. Offline simply means that a specific server is no longer able to talk to the other servers on the Internet. Thus, offline is a matter of perspective.

Server offline

Now, this graph is somewhat dishonest. If you're on a mobile device, all the data goes through a wireless router. If this router goes down, all the phones sending their data through this node go offline. This is why, when your Internet goes down, it's common to ask other people if their Internet is down as well.

Server hierarchy

If you're the only person affected, your device is probably at fault. If other people are affected at the same time, the fault lies higher in the hierarchy...