Sefirat Haomer is given this name, based on the omer, a measurement of barley that was brought to the Beis Hamikdash on the second day of Pesach. The question is why are we focusing on the omer, the measurement, and not on the content of the sacrifice?
This period of time is one of working on oneself in order to be ready to receive the Torah. Chidushei Rabbenu Yosef Nechemyah explains, that omer, stands for עיינים, מעיים, ראש, eyes, stomach and head. These correspond to the three main distractions that leads a person out of this world. Eyes correspond to jealousy, stomach to desire, and head to honor. We count the omer from Pesach, not towards Shavouth. Each day, we acknowledge that we have been successful in surmounting the obstacles we are working on for another day, and yet, another day. 49 days, culminate, a period of self-growth. On Shavouth we offer leaven bread, a sign of human food; we have been successful in becoming a bit more of a mentch.
R. Dunner in Mikdash Halevi points to the idea that omer, is reminiscent of the omer amount that each person received when the manna fell from heaven. In calling this period ‘omer’ we are emphasizing the need to work on the lessons of the manna, which is reinforcing Hashem’s intimate Presence in our lives.
R. Rabinovich in Tiv Hatorah quotes Rashi, that when brining this omer amount, the Kohen would wave it in many directions, influencing the negative winds, and dew from descending on the crops. He learns from this, that even a small action, with even a small amount, has the ability to have cosmic effects. The ‘omer’ period reminds us to grab every opportunity and mitzvah that comes our way; nothing is too small or trivial.