At the time of the broadcast of "Last Of The Time Lords", we were meant to believe that Jack would become the Face of Boe.
Captain Jack explained to the Tenth Doctor and Martha that he was given the nickname "The Face of Boe", coming from Boeshane Peninsula, when he was signed up to the Time Agency. It is also interesting to note, during Captain Jack's goodbye in "Last Of The Time Lords" in which he explains the origin of his nickname, one can distinctly hear the song titled "Boe", which had only been used when referencing or seeing the Face of Boe.
Far in the future, The Face of Boe was an alien of the alleged species Boekind. He was a large face with numerous tendrils around it. He could communicate via telepathy and was rumoured to be billions of years old. His age would make sense if Jack was The Face of Boe, as he would indeed be billions of years old by the time we meet him in "The End of the World". He is also rumoured to be the last of his kind, if any other Boekind even existed. Referencing a non-existent race may be The Face of Boe's attempt at hiding his true origins.
While speaking at the 2008 San Diego Comic-Con, producer Julie Gardner later confirmed that Jack is indeed destined to become the Face of Boe, although at first Russell T Davies was not outright about the fact. Later, in an episode of Torchwood Declassified, John Barrowman, David Tennant and Russell T Davies all said that Jack would become the Face of Boe.
It should also be noted that we may see the birth of the second member of the Boekind species in one Rex Matheson. In the final episode of the Miracle Day series we find out that Rex himself is now also a fixed point that does not die, something brought on by the removal of His own blood only to have it replaced by Jack's so that it can be introduced into "The Blessing" from both sides of the world at the same time.