At the Heart of it All: The Concept of Telepresence (1997) by Matthew Lombard and Teresa Ditton: "A number of emerging technologies including virtual reality, simulation rides, video conferencing, home theater, and high definition television are designed to provide media users with an illusion that a mediated experience is not mediated, a perception defined here as presence". (While this paper concentrates on immersive media - such as virtual reality - it still applies to media like instant messaging -- you can be communicating with low-bandwidth text-only and still have a concept of presence.)
Six conceptualizations in the literature are identified. Presence as...
This is summarised into the Illusion of Nonmediation: "Presence in this view can not occur unless a person is using a medium. It does not occur in degrees but either does or does not occur at any instant during media use; the subjective feeling that a medium or media-use experience produces a greater or lesser sense of presence is attributable to there being a greater or lesser number of instants during the experience in which the illusion of nonmediation occurs".
A lengthy analysis of causes of presence then follows -- but these concentrate on the "realism" of the medium, the closeness of the appearance of the medium to the real world (body suits, three dimensions, etc). However, I think we've found that virtual reality isn't necessary for presence, only that the behaviour of something that appears to be "human" is transmitted through the behaviour of the medium. If the medium is either transparent or its behaviour is mechanical and easily understood, the channelled behaviour can be identified. Only an aspect of the medium need be human -- we're pretty good at identifying agency in the non-human (and often go too far in attributing it...). Also given are causes for the medium itself to be 'present'.
Effects of presence on the user are identified, and areas for further research.
(It seems this paper conflates a number of meanings of 'presence': the feeling that you, the user, are inside a medium; the feeling that a medium can be related to like a person; the sensation - to you - of other people also in the medium (which may or may not be transparent) with you. I don't think it's useful to regard these three together, especially if we're looking at the overall effects of presence. And the overlap between the three uses of the word would explain the over-concentration on VR, especially since - now - we tend to look mainly at the third use, that of multiple human actors in social software.)