Vimeo is a tool similar to YouTube where you can upload videos you created and share with friends and family. You can also watch videos other people have created and You can sign up on the main page for free or log in with your Facebook credentials. There is a page where there are tutorials to teach you how to create videos if you do not already have your own. You can also add channels that you follow with videos you like, create and moderate groups and also organize your videos into albums.
Below is a video I uploaded to Vimeo that I created using FinalCut Pro.
FTI Team Outing 101409 from Jesse Strickland on Vimeo.
Here are some examples of videos that are on Vimeo's site.
There are Vimeo apps that you can download for either your iOS or Android devices that will allow you to watch, create and share videos from wherever you are without needing a computer.
Kids could use this while on a field trip, if they are allowed to use cell phones, to make movies about what they saw and to share with other classmates, other schools or even their parents. It would also be a way for them to save memories of things they have done.