Alice wants to get a message to Bob but she doesn't want to put it on the Internet. Too likely to be captured and, even if they can't decrypt the message, they have metadata about who sent to whom, from where and when. Most of that metadata goes out the window if something is dropped in a public mailbox;
after all, there doesn't need to be a return address, so long as the destination address is legit and there's enough postage.
Alice uses an app to write a secure message to Bob. Alice's message is encrypted, using something akin to PGP (create a random symmetric key, use that key to encrypt the message, encrypt the symmetric key with Bob's public key, create a checksum of the whole thing and encrypt it with Alice's private key, mash all of this together into one digital blob of information) and printed to page-size 2D barcodes. After that, Alice folds it up in an envelope (or rolls it and puts it in a tube) and mails it to Bob.
If it is intercepted and copied (appears to be significantly less common when sent via US Snail), decoding the 2D barcode is straightforward but breaking the encryption is CONSIDERABLY less so.
When Bob receives it, he decodes the barcode, uses his private key to decode the symmetric key, decrypts the message and the checksum, then decrypts the checksum with Alice's public key and checks to see if the sent-checksum matches the locally-calculated checksum. If they match, Alice has effectively signed the message: it could only have come from her (otherwise her public key couldn't decrypt it) and Bob can be reasonably certain it hasn't been tampered with (tampering with it would give a different checksum).
Paperback, a tool to "backup" data to page-sized 2D barcodes, talks about being able to put nearly 6 KB of data (uncompressed) into a square inch of space; that's more than a page of typewritten text. Add some compression to the whole thing and a sizable message could be printed on the back of a postcard. Sure, anyone could image the barcode and decode it but they'd get a bunch of gibberish. Just make sure the ink used to print it won't run if it gets wet (avoid Canon and HP inkjet printers). Most 2D barcode tech lets you add some error correction such that a few messed up pixels won't disrupt the message.
Alice and Bob would each need a smartphone / tablet with imager, or PC with scanner, and a printer for this to work. So long as their device rendered the images, just about any printer, even one at the local library, could likely handle the printing (data would already be encrypted before it went to the printer).
Not the fastest medium in the world but you could send stuff internationally for reasonable rates with minimal risk of surveillance. There was a time when I could get letters between Norway and the midwestern USA in 3 days.