Web threats today take a range of forms: phishing, malware, viruses, trojans, spyware and adware to name a few. What's different today compared to years past is that most of the time, these threats are delivered to your computer from the web (as opposed to an email, or a disk). Even if you are sent an email, it is more likely today that the threat is not attached to the email itself (email antivirus and spam filtering is pretty savvy about that) but rather as a link embedded in the email.
Think of the classic phishing email where you are enticed to click a plausible link - that link is pointing at a URI somewhere, and if it's a URI, Netsweeper can filter it! The delivery mechanism being through a URI somewhere on the web means that web filtering is now a mission-critical technology when it comes to defending your network from the host of web threats encroaching upon it.