After reading what you guys wrote, it dawned upon me that I could think of Here as being a part of the phrase, 'I'm here now...' . That would work, wouldn't it?
That's an interesting idea, Gilbert. Unfortunately, I don't think it will cover all or even most of the cases in which "here" is used as an interjection, where there seems to be no ellipsis at all, "here" merely performing an abstract function as a discourse marker and social cue in diverse contexts.
It's comparable to "now" in "Now, what do you think of that?" It means nothing and elides nothing, but functions, as I see it, as a linguistic gesture. As Gustavo says, it is used to call the interlocutor's attention. It's worth noting that we find this use of "here" almost exclusively in in-person, nonwritten contexts. See also: