said by Mr Anon :
"Trending Videos" will show if you read your bare news feed and enough people on your friends list have viewed the video... I think, or enough people near you or whatever.
Hence why it's called "trending". It means it's popular and the way FB works is, they create connections or links between you and all of your friends (and probably put more "weight" on friends you interact with more*), so you can be certain that "close friends" of yours have watched those videos or read those stories.
* Ever notice wall posts from a friend you don't interact with very often never appear on your feed ? That's where the weighting factor comes in.