When api.php was basically the only API in MediaWiki, calling it "the API" worked well. But now we've got a Parsoid API, Gabriel's work on a REST content API, Gabriel's work on an internal storage API, and more on the way. So just saying "the API" is getting confusing.
So let's bikeshed a reasonably short name for it that isn't something awful like "the api.php API". I'm horrible at naming.