Jefferson was the head of security for the expedition to Krop Tor. According to the Beast, he was a soldier that was "haunted by the eyes of his wife", and was never forgiven by her. Precisely what this means is never made clear.
When the Ood were possessed by the Beast, Jefferson took Rose Tyler, Danny Bartock, and Toby Zed through the maintenance tunnels, which Captain Zachary Cross Flane remotely filled with oxygen manually. Jefferson bought time for Rose and the rest of his team fighting off the possessed Ood. He couldn't make it past 8.1 which was forcibly shut off, as it would otherwise starve the people that were escaping through the tunnels. As no more oxygen could be added to the shut-off tunnel, Jefferson requested Zach to speed up the process of removal, as he chose to suffocate rather than be killed by the possessed Ood.