In the beginning of the game, Dr. Halsey tells the person interrogating her that Spartans are the future of humanity. During the game, the Librarian reveals that Spartans, their armor, and even Cortana, were all part of her plan for humans. She then proceeds to upgrade the Chief in some way. The only two new abilities we know of for sure are that strange form of telepathy he used to hear the Didact and immunity to the effects of the Composer.
What I got out of that is that the Librarian essentially gave him whatever future humans are meant to have genetically that he didn't already have, plus immunity to the Composer. While the Librarian did speak to Cortana, she didn't repair her (which I assume would have been trivially easy for her given how advanced the Forerunners were). This leads me to believe that Cortana's death was seen as somehow important for the Chief's mission.
I predict that the Chief will grow greatly as a character in the next game and whatever he was given in this game by the Librarian will be the single biggest thing to come out of this game in terms of plot.