{{Babel}} is a template for showing the languages that you know, as well as the operating system, keyboard layout, web browser, desktop environment, and text editor that you are most comfortable with. Details of how to use it for its original purpose—showing the languages that you know—are at Wikipedia:Babel.
The page you are viewing right now is the actual Babel template. If you click "edit this page", you will see an invocation of Module:Babel, in Lua, that makes the Babel boxes work. What you're reading right now is just documentation for that code, transcluded inside "<noinclude>" tags so it doesn't interfere with the computer code.
In order to use Babel boxes in another Wikimedia project, you need both the template and the module. Click "view source" and copy all the contents, including the computer code. Create a page called "Template:Babel" on the other Wikimedia project and put the content into it. Do the same for the module.
You will also need to copy over a bunch of templates with names like "Template:User en", "Template:User en-1", "Template:User fr", and so on. Once you've done that, users can put, for example, "{{Babel|en-1|fr}}" on their user page, and the Babel boxes will be displayed.
