A webpage is a single page shown in a web browser. A single video page on YouTube.com is a webpage.
A website is a collection of webpages under a single URL (Uniform Resource Locator). Youtube (youtube.com) is a website.
A web application is a website which offers advanced functionality like a computer program would. An example of a web application would be a web based calendar, or web based email. Youtube.com is also a web application