From Shawn Blanc’s article on WWDC 2014, I particularly liked this bit about Continuity:

But I think Continuity is more than just a better implementation of a cool feature. I see it as a “philosophical” feature as well — it’s a statement that we use our devices for many of the same tasks, and that “work” is device agnostic. Continuity is a way of telling the Apple user it’s okay to expect their devices to always be in sync down to the very mid-sentence of an email in progress.

This is a great way to put it. Continuity is one of those features that “just make sense” – of course my activity should follow me around seamlessly – and it highlights an important point: devices and OSes are different, but the experience should always be consistent and natural.