When the Beit Hamikdash was still standing the primary way to worship Hashem was through the sacrificing of Korbanot. However, presently, when the Beit Hamikdash is destroyed, the עבודה which we direct Hashem to is through Tefillah. Chazal say that our Tefillot today are established based on the Korbanot which took place in the Beit Hamikdash (ברכות כו:)
Knowing that there are two ways of worshiping Hashem, through Korbanot and Tefillah, the question arises as to which is the optimal and primary way to worship. Perhaps Tefillah is the highest form of עבודה, despite Hashem's initial command of bringing Korbanot for some alternative reason. On the other hand, one could argue that indeed Korbanot are the best way to worship Hashem, and that is why Hashem commanded Bnai Yisrael to offer Korbanot. It is only because the Beit Hamikdash is destroyed that we have to settle with serving Hashem through Tefillah.
The Rambam, in his (מורה נבוכים חלק ג' פרק ל"ה) claims that Tefillah is, indeed, the best way of worshipping Hashem. The reason why Hashem made Bnai Yisrael bring Korbanot, initially, is only as a result of the incapability of man to leave behind everything which he is accustomed to doing. The practice of the different nations of the world, at that time, was to bring live animals as sacrifices in their temples. Hashem, therefore did not tell Bnai Yisrael to serve him a manner which they were not used to. The Rambam compares it to what would happen presently if a Navi were to come and tell us to serve Hashem through thought alone, and not through prayer, fasting, or any ceremonial action. It would be unfathomable to us. It is for this reason that Hashem told Bnai Yisrael to bring Korbanot when they came out of Mitzrayim. Nonetheless, Tefillah is the optimal way of serving Hashem for two reasons. Korbanot are limited to one place where Hashem tell us we can bring them (either the Mishkan or Beit Hamikdash). Furthermore, participation is for the most part restricted to Kohanim. Tefillah, on the other hand, can be done by anyone wherever he chooses to do so.
שד"ל )יסודי התורה מ"ז( presents the other vantage point. In his opinion, the greatness and fear of Hashem can only be inculcated into ones heart through Korbanot. He believes that actions make an impression on man more so than saying words. If Hashem would have commanded us to serve him through prayer, song, and the reading of the Torah, it would have paled in comparison to the expensive animals other nations bring as sacrifices to their gods. The impression which everyone would receive would be that our service is דברים בעלמא, "mere words". With such an understanding, Korbanot would undoubtedly be the preferred to Tefilla. The Ramban (ויקרא א:ט) explains that when one offers a Korban, one is essentially sacrificing himself to Hashem.
Undoubtedly, the second approach is representative of mainstream Jewish thought. Rav Yosef Dov Soloveitchik writes (The Halachic Mind p.131) that the Ramban's explanation of Korbanot is "far superior" to that of the Rambam. This explains why we ask Hashem everyday in our Tefilla to restore the Avoda in the Beit Hamikdash. Only there can we relate to Hashem an the highest level possible.