Opening The Archive for the very first time might feel like you've already seen that app somewhere before. And if you used nvALT and/or its predecessor Notational Velocity, then indeed you have! The Archive follows the same basic design cues of its spiritual ancestors—the app window has the omnibar, a list of notes, and an active selected note view. The addition to the classic design is the "Saved Searches" sidebar.
The underlying philosophy and of The Archive, and how it is meant to be used, or at least this is how I see it having spent a bit of time with the app, is based on the work of the 20th century sociologist Niklas Luhmann, who developed the Zettelkasten Method of knowledge management that helped him to manage a lot of information and to be a prolific writer. The German word Zettelkasten literally means a "slip box". And the basic idea is that The Archive is to be a single depository of interlinked notes on any and all subjects, which you would collect in a form of a distilled knowledge that you obtained from reading something. By distilled knowledge I mean notes in your own words as opposed to a simple copy/paste from a source. The Archive, of course, will not refuse to write to disk your note unless it was a creative writing ;-) but, rather, the act of original writing (to a degree) is part of the philosophy, and by doing that you will understand the subject matter better, will remember it better, etc. The interlinking part plays a very important role here, as it is through the links from one note to the other, which may concern completely different fields of study, how thinking is expanded and novel ideas are generated.
To the end of facilitation of interlinking (and you should be aware of this peculiarity right from the beginning), The Archive creates notes with a prefix ID consisting of the year, month, day, hour, minute number, and what that does, it assigns a unique address, so to say, to a note to which you can then permalink in another note.
To summarize, The Archive puts forward some very interesting ideas, and, apparently, the more you commit to them, the more gain you will have. If you are serious about knowledge management and would like to get most of the The Archive, I would suggest that you explore the website of the developers, so as to get more understating about the app and the principles behind it, of which I written only generally here.
Good luck! :-)