Background downloads are downloads that are involuntarily conducted by your operating system. These are usually the updates done on Windows and are automatically downloaded without asking for permission or any interaction with the user. Whenever there are any update requirements, you see them getting updated right away.
Foreground downloads are the kinds of downloads that one has to start by oneself. A very good example of a manual or a foreground download is the one where we click on Get or a Download button so that we can download an update or an application.