Routers are the machines that internet companies use to deliver you pictures of cats. Each router has a special book it writes addresses in (this is called a routing table). But there are only so many pages in that book, and the router can only write one address per page. Because 512 is a magical number within computing circles (because it's the number you get if you start with one and double it nine times), a lot of routers have books with 512k pages in them.
Today, some routers in some parts of the internet needed to write down more than 512k addresses, so they ran out of pages. When it runs out of pages to write addresses in, routers get sad. Sometimes they get very sad and stop working at all, other times they keep working, but because they don't have addresses for all the internet in their special book, there will be some places in the internet they won't know how to get to.
