Aria is the former leader of Giglio Nero Famiglia. She is the mother of Uni and the daughter of Luce. In the Future Arc she was said to be dead due to an illness, most probably the Non-Tri-Ni-Sette/ Negative Seven Rays since she took on the curse. In Gamma's flashback, she and Gamma had a close boss & subordinate relationship (implied in the manga to be romantically intimate).
Aria was the administer of the Sky trial. Her trial involved Tsuna having to do everything she says without a complaint even to go far as protecting her from men possessing box weapons, without knowing if she herself was an enemy. In the end, Tsuna obtains the Sky seal after completing the Trial of Tolerance.