Here's a quick guide to downloading a world from Realms on Minecraft: Java Edition.
First, you need to start the game and click on "Minecraft Realms", there you'll find a list of Realms that you own or have been invited to. It is only possible to download a world from a Realm that you own.
1. Go to your Realms configuration by pressing the button with a tool symbol.
2. From the Realms configuration screen, go to your "World backups."
3. Finally, all you have to do is press the "Download Latest" button and follow the instructions on the screen.
The world you download will be saved with your single player worlds. Downloaded worlds are accessible in single player mode and can be uploaded to a different Realm. If the world you wish to upload was created in a version of Minecraft that is older than the current game version, it might not be compatible with Realms. To solve this, try starting the world in single player mode which will update it to the latest version.
Downloaded worlds are also available in your saves folder located with your Minecraft files; you can learn more about where your Minecraft files are stored here.