The Parim ha'Nisrafim are bulls that are burned, and Se'irim ha'Nisrafim are goats that are burned.

The Torah requires that on certain occasions a bull or goat be brought as a Chatas offering, the blood of which is brought into the Heichal and sprinkled on the Paroches and on the Mizbe'ach ha'Ketores. The flesh of these bulls or goats is entirely burned in the place outside Yerushalayim where the ashes of the Mizbe'ach are deposited.

These occasions are:

(a) The bull and goat offered by the Kohen Gadol on Yom Kippur (Vayikra 16:27).

(b) The bull brought by the Kohen Gadol if he sinned b'Shogeg (Par Kohen Gadol, Vayikra 4:12).

(c) The bull brought by the Sanhedrin if they erred in a Halachic ruling and caused the people to sin b'Shogeg (Par He'elem Davar, Vayikra 4:21).

(d) The goat brought if, due to a mistaken ruling, the entire community worshipped idolatry (Bamidbar 15:22-26).

See Mishnah below, end of 47a, Rashi to 47a, DH Parim ha'Nisrafim, and Rashi to 47a, DH u'Se'irim ha'Nisrafim.

Kol Tuv,

Dovid Bloom