I never noticed Twitter published this "moment" feature until I read the news about Twitter was letting go a few top executives related to this feature.
I checked out some news and found they indeed debuted this feature last October or so. It's already on Twitter web site and mobile app, I just never see it. I asked a few friends about it, none of them noticed either.
It's on the central tab:
There are categories of moments, user can easily switch them by swiping.
The design of moments is sort of visual stories, the only problem is, it doesn't tell a whole story... No one but some curators can make those moments (not sure it's human beings or algorithm). Here is a "moments":
It's sort of Storify wanna be.
Not sure if the "moments" feature is related with twitter's "collection" feature or not. Collection was once a good idea but Twitter ruined it. Rarely I can see people use it, the only use cases are those annoying "social media marketers".
But there are a lot of things Twitter were doing right: effortless publishing, realtime, retweets. The only a thing it doesn't work well is: it can't tell a complete story, it's just broken pieces.
Facebook used to steal quite a few great ideas from Twitter: following model, news feed structure. But now Facebook is far beyond Twitter.