Tandil is an Altmer sorcerer and member of the Psijic Order. He doesn't interact unless spoken to, and will only say "It is time for us to go." He is encountered inside the Hall of the Elements, together with Gelebros and Quaranir during the quest The Eye of Magnus, when they take the eye away from the College of Winterhold.
Tandil shows up with Gelebros and Quaranir, once Ancano has been dealt with. They will take the Eye of Magnus with them, to protect it and Skyrim from the power the eye holds, as people are not yet ready for the power the eye holds.
Tandil will help with the transporting of the Eye. Once they transport the eye, neither he nor any other members of the Psijic Order will be encountered again in the game.