All video content on the Internet requires software to play it. For the most part, sites use Flash to stream video; this is how YouTube works, for example. Other sites use Microsoft's video streaming plugin called Silverlight. To be able to use some of the multimedia content on the Internet, you'll need to install Silverlight on your computer.
If your computer plays videos on YouTube without any problems, and if you never want to watch videos on any other website, you probably don't need Silverlight. However, some major streaming companies, like Netflix, use Silverlight as the backbone of their service. To watch Netflix on a computer, then, you need Silverlight. As of August 2013, Microsoft hasn't yet announced Silverlight 6, which has companies like Netflix looking toward a new solution for streaming in the future. In the meantime, however, Silverlight still powers Netflix and many smaller streaming video sites.