Dear Efraim,

Hana'ah Shel Kilui means that in the course of enjoying the Terumah, through usage, the Terumah is "destroyed"(consumed). According to Tosfos this is permitted (Tosfos Rabeinu Peretz).

The Tzelach learns in Rashi that after it's permitted to a Cohen, a Yisrael can also enjoy it. And Or Chadash learns in Rashi that Hana'ah Shel Kilui is normally forbidden mi'deRabanan but in Rebhe's house it was permitted because of "Tzorchei Rabim".

All the best,

Reuven Weiner