Scripting off generally means no JavaScript, but it could be other programming languages as well.
Webpages may contain JavaScript code.
This code is downloaded by the browser and executed.
Hackers have found vulnerabilities in browsers by use of JavaScript that can allow an outside party full control over your computer.
The normal situation is to receive an email trying to get you to go to a website.
The link could even look legit, like to Amazon, but in reality you won't be directed to Amazon. You will be directed to a site that will download a page with JavaScript in it and then your computer is owned by somebody else.
The other scenario is for a hacker to hack a website and replace the websites normal code with different code. Major League Baseball was hit by this problem.
So visiting MLB.com in the past could have turned your PCs control over to somebody else.
The latest attack vector has been advertisements. You can sign up with Google or Double Click and these companies will automatically ad advertisements to your website. Now there is almost nowhere you can go without the worry of downloading an advertisement containing JavaScript code.
I really wish everybody would stop building websites that require JavaScript. Javascript can make for a better browsing experience, but the risks are huge.