A large portion of Sefer Vayikra discusses bringing different types of korbanos.  The Torah mentions many times that a korban is a "rayach nechoach la'Hashem" (literally, a pleasant aroma to Hashem).  Obviously, Hashem is not enjoying the pleasant smell of the roasting meats.  What is the meaning of this phrase, and what is the underlying reason why we are commanded to bring korbanos? 

Ramban explains the reason behind a korban is that we are really "sacrificing ourselves."  There are numerous ways a person can sin against Hashem: via thought, speech and action.  Therefore, when one sins, he is required to bring a korban.  He leans his hands on the animal, corresponding to a sin he did with his actions.  He must verbally confess, which corresponds to a sin he did with his speech.  Additionally, the innards and kidneys are burned on the mizbayach, which corresponds to a sin done with one's mind, since the kidneys and organs are the origin of thought and desire [See Gemara Brachos 61a-b].  Furthermore, the legs of the animal are burned on the mizbayach, corresponding to a person's hands and feet.  The blood is sprinkled on the mizbayach corresponding to one's soul [See Vayikra 17:14, "hadam hu hanefesh (one's blood is one's soul)].  A person bringing a korban is supposed to be thinking about all these things; that he sinned against Hashem, and it would have been appropriate that his own blood be spilled and his own body and limbs burned.  However, Hashem, in His Ultimate Mercy, allowed this animal to be taken as a substitute for the person.  This is also the reason why one needs to give parts of the korban as matnos kahuna (gift to the kohen), in order that he provide for the teachers of Torah [the kohanim- See Devarim 33:10] so that they pray on his behalf.  Ramban adds that this is the reason why there is a korban tamid (daily offering) on behalf of the entire Jewish nation, because the public as a whole cannot avoid sinning constantly. 

We see clearly, if one merely brought a korban yet did not have a feeling of teshuvah (repentance), he has missed the essence of the korban.  The most important part of bringing a korban is one's thoughts.  The Nesivos Shalom adds that this is why the Torah [Vayikra 1:2] states, "Adom kee yakriv meikem" (A person, should bring from you), as opposed to "adom mekem, kee yakriv" (A person from you, when you bring).  You should view the animal being brought as if it is you! 

The Gemara [Berachos 26b] teaches that since the destruction of the Beis Hamikdash our prayers are in place of the korbanos.  Chazal were very exacting when formulating the Shemoneh Esrei including the fact that it contains 18 brachos.  Why specifically 18?  The Medrash Tanchuma [Vayikra 1] answers, the number 18 corresponds to the 18 joints in a persons' spine.  When davening and bending ones' knees, a person is obligated to bow down to a point at which all the joints of the spine are opened.  Harav Shimon Schwab, zt"l explains it is clear from this Medrash that 18 represents the physical framework of the human being, and thus 18 is the ideal symbolism to express the essence of tefillah; when we daven we are offering our entire body and soul as a korban to Hashem. 

Additionally, after bowing down, the halachah demands the person to stand fully erect when saying Hashem's Name, to express the idea that Hashem is the zokef k'fufim (erects those who are bent over) (Shulchan Aruch 113:7).  This symbolizes that although we are prepared to offer ourselves as a korban, the ultimate will of Hashem is that we not die.  Hashem prefers that we remain alive, living according to His will.  By dedicating our lives and living according to His will, our lives in effect become a living korban to Hashem.  Rav Schwab adds, each time one davens he should also have this overpowering feeling that I am offering this prayer in place of myself. 

Ramban explains the root of the word "korban" is karav [to come close].  Essentially a korban is a vehicle to come closer to Hashem.  Utilizing this tool is not something that we need to wait for until the Bais Hamikdash is rebuilt.  The opportunity presents itself each time we daven!