Folders for the home screen in Android have been there from the beginning and help organize the application icons into groupings that make sense for the user.
In older versions of Android, one would long-press on a blank part of the screen to summon the "Add to Home Screen" menu, then tap "Folder" and "New Folder".
In newer versions of Android, one simply long-presses and drags an icon onto another icon. A folder is then created with those two icons within it.
Folders cannot be nested (you can't put folders inside folders) and only app icons can go in them; no widgets.