Although I'm familiar with the traditional Orthodox Jewish understanding of the word עזאזל, it's my personal belief that the Hebrew word עזאזל, which occurs four times in the Tanakh (Lev. 16:8 x1; Lev. 16:10 x2; Lev. 16:26 x1), is the proper name of a fallen angel, i.e. an evil spirit/ demon. This Hebrew name is very similar to one found in 1 Enoch.
For example, in 1 Enoch 10:8-9, it is written,
8 And the whole earth has been corrupted 9 through the works that were taught by Aza(z)el: to him ascribe all sin.
καὶ ἠρημώθη πᾶσα ἡ γῆ ἀφανισθεῖσα ἐν τοῖς ἔργοις τῆς διδασκαλίας Ἀζαήλ· καὶ ἐπ’ αὐτῷ γράψον τὰς ἁμαρτίας πάσας
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While some rabbis traditionally believe עזאזל to refer to a particular place, yet other Jewish rabbis such as Ibn Ezra and Moshe ben Nachman did in fact assert that עזאזל was the proper name of a demon.
Rabbi Avraham Ibn Ezra (ראב"ע)
In his commentary on Lev. 16:10, Ibn Ezra wrote (in part),
ואין צריך, כי המשתלח איננו קרבן כי לא ישחט ואם יכולת להבין הסוד שהוא אחר מלת עזאזל, תדע סודו וסוד שמו, כי יש לו חברים במקרא ואני אגלה לך קצת הסוד ברמז, בהיותך בן שלשים ושלש תדענו.
which is translated as,
But there is no need (for this comment), for the [goat] sent is not a sacrifice, since it is not slaughtered. And if you can understand the secret of the word that is after עזאזל, you shall know the secret and the secret of his name, for it has parallels in scripture, and I shall reveal to you some of the secret with a hint: when you are thirty-three years old, you shall know it.
What does Ibn Ezra mean? Why thirty-three years old? The עזאזל first occurs in Lev. 16:8. If you count thirty-three verses from Lev. 16:8, you end up at Lev. 17:7. In Lev. 17:7, it mentions the Israelites sacrificing to שְׂעִירִם. Ibn Ezra is hinting that עזאזל is a demon, perhaps one of the שְׂעִירִם. In his commentary on Lev. 17:7, regarding the שְׂעִירִם, he states, הם השדים, that is, "They are shedim" (cp. Deut. 32:17). There seem to be some apparent similarities to 1 Enoch.
If you recall in 1 Enoch, it states that all sin is to be ascribed to Ἀζαήλ (1 Enoch 10:9). And, what happens on Yom Kippur? One goat is kept alive, while the other goat is sent to Azaz'el after all the sins of the entire Jewish people are confessed upon it by the High Priest (see Rabbi Moshe ben Maimon: Mishneh Torah, Hilkhot Avodat Yom ha-Kippurim, Chapter 2, Halakha 6).
There's another interesting fact. Azaz'el's goat (לַעֲזָאזֵל) is said to be sent הַמִּדְבָּרָה (ha-midbarah), "to the wilderness." The LXX translates this as εἰς τὴν ἔρημον (eis ten erēmon). Coincidentally, 1 Enoch describes τὴν ἔρημον ("the wilderness," "the desert") as the very location of Azaz'el.
In 1 Enoch 10:4-5, it is written,
4 And again the Lord said to Raphael: 'Bind Azazel hand and foot, and cast him into the darkness: and make an opening 5 in the desert, which is in Dudael, and cast him therein.
Καὶ τῷ Ῥαφαὴλ εἶπεν Δῆσον τὸν Ἀζαὴλ ποσὶν καὶ χερσίν, καὶ βάλε αὐτὸν εἰς τὸ σκότος, καὶ ἄνοιξον τὴν ἔρημον τὴν οὖσαν ἐν τῷ Δαδουὴλ κἀκεῖ βάλε αὐτόν
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Rabbi Moshe ben Nachman (רמב"ן)
In his commentary on Lev. 16:8, Rabbi Moshe ben Nachman makes a similar assertion to Rabbi Ibn Ezra concerning the meaning of the word עזאזל.
והנה התורה אסרה לגמרי קבלת אלוהותם וכל עבודה להם, אבל ציווה הקב"ה ביום הכיפורים שנשלח שעיר במדבר לשר המושל במקומות החורבן, והוא הראוי לו מפני שהוא בעליו ומאצילות כוחו יבא חורב ושממון כי הוא העילה לכוכבי החרב והדמים והמלחמות והמריבות והפצעים והמכות והפירוד והחורבן, והכלל נפש לגלגל מאדים, וחלקו מן האומות הוא עשו שהוא עם היורש החרב והמלחמות...ובחלקו עוד השדים הנקראים מזיקין בלשון רבותינו, ובלשון הכתוב להלן יז ז): שעירים.
which is translated as,
Now the Torah has absolutely forbidden the acceptance of gods and all worship to them. However, the Holy One, blessed be He, commands us on Yom ha-Kippurim (the Day of Atonement) that we should release a goat in the wilderness, to the "prince" who rules over wastelands, and this (goat) is fitting for it because he is its master, and destruction and waste emanate from his power, which in turn is the cause of the stars of the sword, wars quarrels, wounds, plagues, division and destruction... Also in his portion are the devils called "destroyers" in the language of our rabbis, and in the language of our scriptures, "se'irim" (demons).