I paused a video in YouTube's app for Android and got this message: "paused videos keep buffering if you leave the app". There's a background buffering feature and YouTube shows the how much data has been buffered. For example, "buffering 11.8/39 MB". YouTube videos are actually cached, so that's the reason why YouTube's cache can become huge.
When YouTube caches the entire video, you'll receive a notification which shows that the video is "ready to watch".
This is useful if you have a slow Internet connection: play a YouTube video, pause it, leave the app and wait until the video is cached. Then you can watch it.
An article from Indian Express mentioned in December that "Google will introduce pause buffer feature soon allowing users to pause video, leave it to buffer, even leave the app or site and let it continue buffering". Google CEO Sundar Pichai delivered a keynote speech at a Google India event in New Delhi and announced a lot of interesting features: "tap to translate" will be released this year, "Google will crowd source the data for its translate feature", "1.4 billion Android users in the world", "WiFi at 100 railway stations in India by December 2016", "Internet access to Indians in their own language is the focus for Google in India".