Todah And Shavuot

This post is based on a shmuz by Rabbi Yosef Elefant.

What does the avodah of sefirah have to do with the korban omer? 

The Ramban (23:17) says והנה בחג השבועות שהוא יום מתן תורה יביא הקרבן בדין תודה כי הוא יום העצרת והמשכיל יבין וזה סוד מה שאמרו רבותינו (ויק"ר ט ג) כל הקרבנות בטלין וקרבן תודה אינו בטל לעולם וכו' כי בו מצה וחמץ כענין בעולם הבא.  What is unique about this combination of chametz and matzah and why is it offered in the todah?  The ultimate תודה, thanks, is to recognize that even the bad, the חמץ in life also plays an important role in one's life.  That is the ענין עולם הבא where it is clear that everything is a manifestation of  the יחוד of Hashem.  The todah demonstrates that opposites, chametz and matzoh coexist.  What does that have to do with Shavuot , which the Ramban says is the same idea as the todah?  As elaborated in the Sifsay Chayim Moadim 2 pg. 22 footnote 11:

The Maharal (Teferet Ch. 24-25) explains the conversation between Moshe and the malachim recorded in the Gemarah if the Torah should be given to mankind is that the answer of Moshe is that the Torah must be given to gashmiout.  The Maharal expounds at length that every שכל requires a כלי of gashmi to hold it.  That's why the omer is a korban of animal food because the Torah is given to the gashmiout of a person.  As he concludes in Ch. 25, לכך היה הקרבת עומר בט"ז ניסן מן השעורין. שהשעורין הם גופניים, כי הם מאכל בהמה. וקרבן זה ביום ראשון של ספירה, כי הגוף הוא מוכן לקבל מדרגת השכל, וכמו שהתבאר לפני זה, כי אי אפשר לתורה רק שיהיה לה מקבל גשמי.  The process of kabbalat haTorah, of sefirat haomer, starts with a korban of animal food because that is the reason why Torah was given to mankind because he is made up of gashmi.  That is why the korban of the omer is the hakdamah to the avodah of sefirat haomer because that is what brings the Torah to mankind.   

On Shavuot we celebrate the fusion of the ruchni and the gashmi.  That is the chametz and the matzah.  Torah.  It is a celebration that the fusion of opposites is what brings out the power of the Torah.  That is the message of the todah, the recognition of the need for the chametz and matzah, the ultimate unity, which is expressed in Olam Habah.  

For a different explanation see here.