It's a more than decent alternative to libraries like Angular or React for building web interfaces. I've followed a few tutorials and find it really inspiring. I hope it catches on.
Large companies have used this because, like Ractive, with which it kind of competes, you can produce something very quickly (Ractive was initially developed for internal news room use). Alibaba used Vue for Singles day, Nintendo for its forum, etc. Using it for quick-turnaround work is a breeze.
Writing components in single files is mighty nice (w/ or w/o pre-processors): http://blog.evanyou.me/images/vue-component.png
And it looks like a flux approach is in the works: https://github.com/vuejs/vuex