Most web sites utilize Youtube for marketing purposes these days (or at least they *should*). Integrating videos is fairly straightforward, too; Youtube wouldn't be where it is today if it hadn't made embedding videos on web sites and on social media extremely simple and straightforward.
That said, when Youtube becomes a major aspect of a business' marketing (and, I'm talking about managing a growing list of hundreds or thousands of videos), then managing the web integration in a more sophisticated way can offer benefits for a web site. So, I wanted to cover that in a fairly broad way, but also show some basic examples of how to do it in a way most site owners are as aware of.
If you're a web developer, the entire article should interest you. If you're a business owner interested in ROI, I recommend skipping to the end where I offer advice on whether it makes sense to consider pursuing a Youtube API integration with your web site.