An assembler for the Burroughs 220 written by Melvin Conway. The name "SAVE" didn't stand for anything; it was just that you lost fewer card decks and listings because they all had SAVE written on them.
To copy data to a more permanent form of storage. The term is commonly used for when some kind of document editing application program writes the current document from RAM to a file on hard disk at the request of the user. The implication is that the user might later load the file back into the editor again to view it, print it, or continue editing it. Saving a document makes it safe from the effects of power failure.
The "document" might actually be anything, e.g. a word processor document, the current state of a game, a piece of music, a website, or a memory image of some program being executed (though the term "dump" would probably be more common here).
Data can be saved to any kind of (writable) storage: hard disk, floppy disk, CD-R; either locally or via a network.
A program might save its data without any explicit user request, e.g. periodically as a precaution ("auto save"), or if it forms part of a pipeline of processes which pass data via intermediate files. In the latter case the term suggests all data is written in a single operation whereas "output" might be a continuous flow, in true pipeline fashion.
When copying several files from one storage medium to another, the terms "backup", "dump", or "archive" would be used rather than "save". The term "store" is similar to "save" but typically applies to copying a single item of data, e.g. a number, from a processor's register to RAM.
A "save" operation saves the document in its native format, e.g. a proprietary word processor format, whereas "save as" (or "export") saves the same data in a different format, e.g. a plain text file.