An Adobe Target Mbox is a little bit of Javascript on a page that helps you run a test or experience for users on a given page. It does a lot of things including tracking users, tracking results, administering the test, and changing the code to make the test visible to the user.
Originally, mboxes were designated areas (like a specific div) within a webpage where you might run a test on that specific area. You could have multiple mboxes on a page. Therefore you could target and test each area with an mbox. This was helpful if you wanted to run a test just the contents of that div. For example to switch out and test the hero image or a banner. But it wasn't helpful if you wanted to test other areas of the page.
Several years ago, Adobe moved to Global Mboxes. A global mbox is a single mbox on the page that can test anything. Basically, you install a global mbox on every page on your site. This allowed you to test any page of your site. The other benefit of the global mbox was that it wasn't limited to just one area of the web page. Along with Global mboxes, Adobe introduced the Visual Experience Composer. The VEC is a WYSIWYG which takes advantage the the global mbox and allows out click on and pick any div on a page that you want to change or test. This made it a bit easier for marketers who weren't as experienced at coding. The global mbox also gave more flexibility to experienced coders to write more complex javascript and run more complex tests.