What's an archive?

Conceptually, or at least as far as Google Play is concerned, an archive represents a phone (or a tablet for that matter). You can create as many archives as you like (e.g. one per device you own).

Functionwise, an archive acts as a download folder that can contain multiple versions of downloaded apps and that is able to automatically update all contained apps.

In other words: think of an archive as the place on your harddisk, where you keep a backup of the apps on your phone (or tablet).