Before computers, business was largely conducted on paper, and one might arrive at the office to find several documents or pieces of mail waiting on one’s desk. And when those documents needed to be returned or sent elsewhere, you took them yourself, mailed them, or asked someone to do so for you. For ease of organization, it was common to have two paper-sized receptacles on one’s desk: an inbox, for all incoming documents, and an outbox, where your finished or outgoing documents went, and would be picked up regularly.
How did those documents know where to go? Their destination could be spoken, of course, or attached with a scrap of paper using a paper clip, or with a sticky note. Offices with lots of moving documents would also have envelopes with columns of “to” and “from” fields that you would use, crossing out the last one and putting your own. (These have, perhaps thankfully, not found their way into the modern visual idiom.)
Modern email and messaging clients have adopted a similar aesthetic, with email arriving to the inbox and so on. And in fact, although nowadays we tend to assume electronic communications are sent as soon as we hit the button, it used to be the case (and still can be depending on configuration) that unsent mail and messages went to sit in an “outbox” until the mail client was prompted to sync with the server, or the server contacted the client to ask for any new messages, or until the user connected to the internet.