as the others have said, you can't store files on the aTV.
look at Infuse or Plex
Plex requrires a computer running their server (windows, Mac or linux)
Basically turns your computer into it's own personal netlfix like service.
It will also automatically add data (like title, descriptions, cast and crew) to all your files.
and you can watch from multiple devices (start a show on the aTV, stop, and then pickup in the same place on your phone)
you can have multiple accounts each with their own watched status, and even share with friends outside your home if you have enough bandwidth.
It will also convert files automatically if they won't play natively on the player you're using (like a 4k video on a 1080 aTV)
just for kids videos this might be a bit much.
infuse will access a network share directly on the aTV, so no specialized server program needed, just a computer and a folder shared using windows file sharing.
infuse can also add metadata, (I don't use this) but I believe it's local on the aTV,
for both Plex and infuse, you could use a NAS instead of a computer.
Either a standalone NAS unit, or a RasPi with your choice of OS and some USB drives.
There are NAS devices that will run Plex on them. and there is also a Pi image for Plex.
One thing to keep in mind, for the NAS or Pi, you want to make sure your files are compatible with the aTV player, since there's not a lot of horsepower to convert them on the fly.