A Video Player is a plug-in that allows you to play a video you have embedded in your website.
There are several plug-ins that work very well. For WordPress I use Huzzaz Video Galleries, which is free and allows for several different ways of displaying your videos if you have more than one.
For a single video I love embed.ly. It gives you a Short Code to embed on the WordPress page and couldn’t be any easier. It’s also not customizable, but it will honor the YouTube (or Vimeo) settings you have established.