Our tradition has it that maamad Har Sinai was really the culmination of Yetzias Mitzrayim. The Mishna (Avos 6:2) comments on the phrase "charus al hlauchos" (Shemos 32:16) that we shouldn't simply read "charus" (that the aseres hadibros were engraved on the stones) but rather we should also read "cheirus" (freedom), implying that one is only free if he learns Torah. Some people are slaves to an outside master; others are slaves to their own desires, i.e. they are not in full control of themselves. Hakadosh Baruh Hu told us (Kiddushin 30b) "barasi yetzer hara, barasi lo Torah tavlin". The only antidote to this problematic condition (of improper desires) is Torah. Learning Torah and regimenting oneself in keeping mitzvos gives one the ability to gain control of one's own desires.
The posuk in Koheles (10:17) praises "the country whose king is a free person". The Zohar understands this to be referring to Eretz Yisroel. It is the praises of Eretz Yisroel that Hakadosh Baruch Hu is officially its King, and Yerushalayim, the official capital of Eretz Yisroel is known as kisei Hashem (the throne of G-d - see Yirmiyahu 3:17). According to the interpretation of the Zohar, Hashem is referred to as "ben chorin". He is the one who gives man the ability to become free.
From the very outset, when Hashem appeared to Moshe Rabbeinu from the burning bush, He told him "when you will lead the Jewish people out of Egypt you will serve Me on this mountain."[1] Moshe Rabbeinu didn't feel that he was qualified to lead the drama of the exodus since he had no experience in politics. Whereupon Hashem answered him that the main purpose of yetzias Mitzrayim was not so much to gain political freedom for the Jews, that a statesman should be required to lead, but rather the whole purpose of the exodus, (and the true meaning of freedom) is to lead to Torah study. Although Moshe Rabbeinu was not a polished statesman, he was cut out to be a top notch melamed. And this was the meaning of the phrase, "taavdun es haElokim al hahar jazeh"; the term avodah in this pasuk refers to limud haTorah. The Rambam (Sefer Hamitzvos, Aseh 5) quotes from the Sifrei that the term "avodah" in the Torah can refer to one of three things: offering of korbanos, tefillah, and Torah study - "avdeihu b'Toraso". The common denominator among these three (as opposed to all other) mitzvos seems to be that the individual is in the state of lifnei Hashem[2] and is directly interacting with Hashem. When one offers a korban, it is not as if one has sent via UPS, and the driver leaves the package with the superintendent who will later hand it over to the addressee. The rabbis in the Talmud (Taanis 26) comment, how can one's korban be offered when the baal haKorban is not present? It is as if Hashem were there in person receiving the gift. In prayer as well, Rambam writes (Hil. Tefilah chap. 4) that when one davens he is lifnei Hashem, and should carry himself as if he were in heaven in the presence of G-d, speaking to Him directly. It is not as if one sends a letter requesting assistance to someone else. When one davens, he is directly interacting with Hakadosh Baruch Hu.
The same is true of Torah study. The rabbis had a tradition that "miyom shecharav beis hamikdash ein lo l'Hakadosh Baruch Hue la daled amos shel halacha - from the day the Temple was destroyed the only place where Hashem can be found is in the four amos of halacha" (Berachos 8a). When the Temple stood, one would visit there and be in the presence of Hashem - the Beis Hamikdash was the "house of Hashem". After the Temple was destroyed, one can best enter into a state of Lifnei Hashem by learning Torah. The opening word "anochi" of the aseres hadibros is taken be the Talmud (Shabbos 105a) to represent (by the way of rahsie teivos) the idea that "ana nafshi ksivas yehivas" - by My writing down My Torah, I have given over to you the essence of My soul. The Torah is a description of Hashem.
The Talmud tells us that one who delves into Torah study, the shechina will be there with him[3]. When Hashem told Moshe that the exodus will lead up to "avodah" on Har Sinai, this was referring to the Torah study on the occasion of maamad Har Sinai. The unique status of these three mitzvos (korbanos, tefillah, Talmud Torah), that they alone should be referred to as avodah , seems to be that only in these three is there direct interaction with Hakadosh Baruch Hu, like an eved serving his master directly.[4]
[1] See Meipeninei Harav, kuntras sefiras haomer, #10
[2] See Ramban (Breishis 4:13-16) that Kayin understood on his own that his punishment would be that he would no longer be allowed to interact directly with Hashem either by praying or offering a sacrifice; the Torah confirms that indeed that was his punishment: "vayeitsei Kayin milifnei Hashem"
[3] Avos 3:3, Tamid 32b.
[4] The Talmud (Berachos 34b) relates that when the child of the chief rabbi, R' Yochana ben Zakai, took sick, R' Yochanan asked R' Chanina ben Dosa (his student) to pray for the child's recovery. When the child got better, and it was obvious to all that the recovery was due to the prayers of R' Chanina, R' Yochanan commented that even if he were to daven all day long he would not be able to accomplish with his prayers what R' Chanina accomplished with his brief prayer. R' Yochanan's wife asked her husband how can it be that R' Chanina (his student) is greater than him? R' Yochanan responded that R' Chanina is not greater in Torah learning, but I (R' Yochanan) an like a sar (minister) in the cabinet of a king who is not free to visit the king and speak to him whenever he wants to. But R' Chanina is to be compared to the king's servant (eved) who can go in and out of the king's private room freely whenever he chooses and can always speak to the king. We see that the concept of "eved" is one who serves his master directly - face to face.