A lot of websites still use Java on the server-side, but not necessarily piped down to your browser. A security flaw like this really impacts corporations more than most regular web surfers realize if it needs to be disabled/removed. Mobile devices use Java, maybe your big screen TV even. It's found in a lot of technology, but this warning only applies to computers connected to the web.
You may find that certain features of your favorite website may not work for a while until a patch is distributed or they come up with a workaround.
Java was Sun's love child but ever since Oracle bought out Sun, Java's been kind of a step-child that doesn't fit in with the rest of the Oracle family so it doesn't get the attention it deserves.
This isn't the first major security flaw discovered recently with Java. ALL software has flaws so it's mostly the effort put into responding to and also proactively looking for flaws that sets the bar on security. Remember how Microsoft products were the butt of jokes not that long ago for the number of high profile security flaws that kept surfacing? Well, Microsoft invested a lot of money and attention to the matter and now how often do you hear about major MS security flaws with their IIS webserver, Internet Explorer, etc?