As long as you have cloud storage enabled you can go into the "System" menu, select "Storage" and choose the Hard Disk Drive. In the "Games" folder there should be a "Minecraft" folder. Open that. Find the saved world you want to back up. Highlight it and then select copy. When it gives you the menu for selecting where to copy it to simply choose the cloud storage.
If that's hard to follow here is a handy video tutorial:
In addition to what Urban_Blackbear has instructed, there is one caution - you must be signed in using the same gamertag that "owns" the world before you can copy or move it to another device (USB or cloud).
If that's hard to follow here is a handy video tutorial: