Ah, I remember the little Flip Mino, a pocket HD recorder that took the world by storm and then sank beneath the waves of competition from smartphones that could perform a similar task.
The app, called Givit, is free at the App Store. New users get 5 GB of free online storage for their creations. You begin shooting video(s), then edit by combining multiple clips, adding motion effects, music and transitions. What's cool is that you can highlight a scene as you shoot it and quickly get back to it with a tap.
When you are done, you can share via Facebook, YouTube or email. I like the email option the best, as it's less public and more personal.
Advanced paid plans will let you increase your storage, but most users should be able to get by with what is offered for free.
I created a few videos and the process was pleasantly straightforward. Built-in help pops up when you first try the app, and it can be easily recalled. I had a few crashes on my iPhone 4S when I first started using the app, but a reboot ended that.
Givit wants to be Instagram for video, and it has a chance to succeed. The app is intuitive, easier to use than similar apps, and it has popular social functions built in.
The app is not universal, but can run on the iPad and also the iPod touch. It requires iOS 5 and is iPhone 5-ready.