The Sefat Emet asks why the Omer offering in the Holy Temple consisted solely of barley, but for the Two Loaves offered on Shavuot wheat bread was brought. He explains that this matter alludes to the spiritual process that the Children of Israel underwent during this period.
Barley is food for animals; wheat is food for humans. In the period between the Exodus from Egypt and the Giving of the Torah, the Children of Israel elevated themselves from animailstic desires and behaviors to the level of ethical, refined human beings. Therefore, for the commandment of the Omer, barley is harvested, for they were on the level of animals at this stage. Then, after fifty days of refining their character traits, they reached the level of man and offered wheat loaves, food for human beings.
The Ari z'l is quoted as saying that when the Children of Israel left Egypt, they were immersed in forty-nine levels of impurity, and the Holy One, blessed be He, elevated them two levels each day to the source of sanctity.
How did they raise their spiritual level in just 49 days every day?
It must have been through perfecting their middot (character traits) this let them reach an extremely high level of unity at Mt. Sinai that according to Rashi's commentary: they camped there like 'one man with one heart'.
The omer period is dedicated to perfecting our character traits which is why the 24,000 students of Rabbi Akiva were punished during this period because they did not improve their traits and achieve the required unity.
Let us try our best to improve ourselves and our relationships with others!