How Does a You Tube Video show up on an iPhone?

I do not have an iPhone. My wife has an iTouch. If you click on link for a You Tube Video, how does it show up? Does it take you to a You Tube site, or does the video come up and fill the screen?

Im not very familiar with the itouch, but I know on the iPhone, when you buy it the youtube app is a preset app on it, all you have to do on it is go to the app and look up the video and it should do the rest on its own. If the itouch didnt come with the app then purchase it to make your youtubing that much easier!
Hope this helped