The Non-Wayback Internet Archive is simply a very large collection of millions of items.
In its purest form, an item is simply a directory on the Archive's servers, with a unique name referred to as its identifier. This uniquely-named directory will contain several system files (for metadata, system information, hashes, etc.) and the rest will be up for grabs and represent the actual data in the item. Items can have subdirectories and even entire filesystems beneath them, although there are increased issues if there are too many files or the items themselves are too large.
These items come from several sources: the Internet Archive's employees/contractors/projects, partner organizations or efforts, and individual users that can add new items into the open collections.
The items are classified under several "media types" that dictate how the content of the item will be presented in the details page/theater, the page for that item that is located at https://archive.org/details/ITEM. Using the web interface or a command line program, it is possible to engage with the contents of the items all different ways.
Items can be grouped together into 'collections, which are simply internal lists of items. (It is also possible for a collection to be put underneath another collection, making it a "sub-collection". To make things even more confusing, the Archive considers each collection an Item.