These are DNS attacks, which are not attacks on websites. They do not bring down any website, nor do they place malware on them. There is a risk though, a non-HTTPS site can be easily redirected to a different website without detection and that can cause you issues. If you go to a site that uses HTTPS and you get a security warning from your browser, back away! If that happens to a big site like Amazon or your bank, either there was a DNS or other man in the middle attack trying to take you elsewhere, or someone dropped the ball and let a certificate expire.

What DNS attacks do is keep your browser from resolving a URL(ie psychcentral.com) to its IP address, which is what is needed to be able to send and receive data. Psych Central is still running, your browser just can't reach it. Think of it as removing phone books. The businesses are still there but unless you know the phone number, you can't call them.

Whether you are affected has to do with what DNS servers you use, typically the default servers used by your ISP. How many DNS services the website uses will lower the odds that the website is affected too much.

That explanation is missing a lot of technical detail but hopefully is easy to understand.

Edit: Didn't notice this was a 10 day old topic, well hopefully it is still useful or informative.