“The best way to infect thousands of computers is to set up a malicious website. Better still, hack a popular website and insert malicious code. That way, thousands of website visitors will be affected when they visit the website. Badware is the name given to the malware present on websites – in the site code or in the malicious advertisements or malvertisements being displayed on the website.” – TWC

It basically ignores your choice as to how your computer or your network connection is used, and it distributes malware either because it is intentional or because it became infected unintentionally.

How to know if a site is infected?

1. Fail-proof: Reputation based (remember, the shortcoming here is when your software recognizes this: Depends on updating and crowd reporting). When you attempt to visit the infected site using any of the standard browsers, you will get a message that visiting the site may be dangerous. The wording of message can be different, but you will see an alert about the website. Since there can be false positives, most browsers give you an option to continue visiting the website at your own risk. Your security software too could throw up a warning, that it could be dangerous visiting a website.
2. Searching for a website using popular search engines give out a description that is not related to the website. If you have been visiting the website before, you can instantly tell that something is not right after seeing the site description in the search engine result pages (SERPs).
3. If you are a website owner and have webmaster accounts with Google, you will receive notifications about possible malware on your website.
4. You find that file permissions have been changed.
5. You may encounter unwanted and unexpected redirects when you click your website name when it appears in search engine results pages.
6. In some cases, you can see new users on the webmaster dashboard; in other cases, the permissions for users may have changed. – ibid

Browsers: IE has SmartScreen Filter, and an XSS Security feature preventing cross-site scripting.

If you browse to an infected site, you get this:

Chrome has this in settings:

So, it's quite important to have the proper options checked off, and to keep your security software and browsers updated DAILY.

Sources:

http://www.thewindowsclub.com/what-is-badware

http://www.thewindowsclub.com/how-to-enable-or-disable-smartscreen-filter-in-internet-explorer-9

http://www.thewindowsclub.com/smartscreen-filter-xss-security-features-in-ie-8