It's never really explored other than what it does, bringing him back to life as he was when he `died`. The power that granted Jack his immortality supposedly made him a `fixed point in time` and unable to change from that point, though it was later revealed that he was very slowly aging regardless (apparently to cover John Barrowman`s own aging). I doubt he`d be a part of the TARDIS and therefore related to Time Lord technology / physiology in some way, given how the Doctor instinctively avoids him (at least at the beginning).
Something of a recurring theme in RTD's Who writing is how much immortality sucks. Aside from living on when all your loved ones age and die, the nature of how one doesn't die is usually pretty gruesome. From how Jack re-forms painfully from a big of bits and slowly ages anyway, to Cassandra's body, to how the Doctor bemoans each regeneration as feeling as bad as death... It's funny how THAT concept is explored more than the mechanics of the immortality itself, but then again it's sci-fi by writers, not scientists.
Mark