What is ''Azazel"?
Ramban #2 (citing the Ibn Ezra - and elaborating) 5 : It means that the goat goes - the goat represents Eisav, 6 who carries the sins of Yisrael out to his domain (the desert). In fact, the Sa'ir la'Azazel is in the form of a bribe to Sama'el, 7 the angel of Eisav, to dissuade him from prosecuting Yisrael on the day of judgment. 8
Moshav Zekenim (from Yuma 67b): The word alludes to Uza and Aza'el, two angels that descended before the flood - "va'Yir'u Bnei Elokim Es Benos ha'Adam" (Bereishis 6:2), i.e. it atones for Arayos.
Moshav Zekenim (citing Agada): It is an angel that used to prosecute against Yisrael on Yom Kipur. Hashem said, if you were among them, also you would sin! The angel descended, and had Bi'ah with Na'amah. Hashem decreed that he never ascend, and each year we send a goat to him to recall the episode and silence all prosecutors - they see what happened to one who prosecuted against Yisrael!
Rosh (22): It is Mars, one of the seven [Kochvei Lechet] that serve this world. It causes murder through the sword. The Torah said to give a bribe to it, lest it strike us.
Perhaps this means 'rocky'.
As implied in Pasuk 22 (Rashi).
Ramban: As a matter of fact, "la'Aza'zel is the acronym of 'le'Az Azal' - 'it goes to a harsh place. Rosh - the Ez (goat) Azal (goes, to a mountain).
Hadar Zekenim: It is sent to a barren land, for the Aveiros that it carries cause that nothing will grow there.
The Ramban's elaboration is based on a Midrash Rabah.
Indeed, Pirkei d'R.Eliezer (46) relates that, when Samael (who carried out all Yisrael's sins on the Sa'ir la'Azazel) sees that Yisrael are without sin, he exclaims in amazement how special are Hashem's people and how they resemble the angels - inasmuch as, on Yom Kipur, they go barefooted, they do not eat and drink, they remain standing, they are at peace with each other and they do not sin - just like angels!
What is the procedure of the lots?
Rashi and Targum Yonasan: Aharon places one of the goats on his right, the other, on his left; then he puts his hands into the box 1 (that is lying in front of him) and takes one lot in his right hand, and the other, in his left, 2 and places the one in his right hand, on the head of the goat on his right - and announces 'la'Shem Chatas'; and the one in his left hand, on the head of the goat on his left - and announces 'la'Azazel'.
What is the purpose of the lots?
Ramban: Had Aharon decided on his own which goat is for Hashem and which goat is for Azazel, it would be akin to giving the former to Hashem, and the latter, to Azazel. 1 But now that he drew lots, it is akin to giving both goats to Hashem, and it is Hashem who gives it to Azazel. 2