What's happening on Monday is not a 'virus hitting,' per se. Allow me to provide the non-technical form.
First off, as background, the Internet as a whole doesn't know domain names. Think of the telephone network; everyone has a number, but the phone system doesn't know that 555-1212 maps to Fred and 867-5309 maps to Jenny; you don't pick up the phone and dial 'J-E-N-N-Y,' but rather you look in a phone book for what Jenny's number is, then dial that. The internet works the same way; "asoiaf.westeros.org" is not an Internet address that you can connect to; you have to actually 'dial' the machine's address, which is 108.168.195.26.
Because numbers are a pain to remember, we have what's called the Domain Name Service. Your machine will have DNS servers set up (which, often, will just be your home router, which will then send queries outwards). When you enter 'asoiaf.westeros.org' into your browser, your machine contacts that DNS server and says 'Hi, I need to reach asoiaf.westeros.org, what's the number?' And the DNS server either knows (and answers), or goes out to ask a DNS server that *does* know. (Bonus note: this is why server moves can take a while before everyone sees a new site.)
So, on to the Monday issue.
Some time ago, there were several trojans which targeted both Windows and Mac. (Note: viruses will spread on their own, while trojans require tricking the user into running something.) Among other things, these Trojans changed the DNS servers your machine (and in some cases, your router) would go to look up addresses on.
This meant they could control your Internet experience. For instance, if you went to Google.com, they could resolve 'www.google.com' to their own servers and take your query, pass that to the real Google, get back the answers and put a few of their own paid/malicious links into the search results. They could misdirect or break all your searches for antivirus programs and so on.
Now,
some time ago, these folks got shut down. But many machines had their DNS changed over, so the FBI took those DNS servers and set up real ones there, so that everyone wasn't cut off. But running those servers takes time and money (they are taking a fair amount of traffic!), and they were going to shut those down months ago. But a court ordered them to keep the servers up a while longer, to give folks more time to clean up and ensure they weren't still using bad DNS servers.
That came to an end today.
So if you *did* get your DNS settings changed by the trojan and you *haven't* fixed them, when the servers shut off you would have found you still had Internet access but that your computer no longer could resolve a name to an address; if you entered 'asoiaf.westeros.org' in your browser, instead of 108.168.195.26 you'd get back a SERVFAIL, meaning the server couldn't answer. Same for Google.com, Facebook.com, whatever else.
On the other hand, the servers were shut down already this morning, so chances are that if you're seeing this site at all to read my message, either a) you're fine,

you're reading from someone else's machine or your phone, or c) you still had asoiaf.westeros.org in your name resolution cache, and the Internet will vanish shortly.
I'm putting my money on a, statistically.