Here is how to backup and restore your saved games or worlds in the Windows 10 edition (from the Windows store) of Minecraft. It is actually pretty easy once you know where the save games are, although it would be nice if they would save to Onedrive or cloud so that they were automatically backed up.
- Open %userprofile%\AppData\Local\Packages\Microsoft.MinecraftUWP_8wekyb3d8bbwe\LocalState\games\com.mojang\minecraftWorlds
- Copy the folders in here e.g. to your Onedrive. These are your worlds.
- Install Minecraft on the PC
- Login using the same Microsoft account
- Open the above location, and copy the folders in there
- Now just run Minecraft and you should see your worlds