The first time the Jewish people counted during the period between Passover and Shavuot was when they left Egypt and were preparing themselves to receive the great gift of G-d's Torah at Mount Sinai.
At the time they were on a journey not only toward Mount Sinai and ultimately the Holy Land, but they were also on their own personal journeys of self-refinement and purification.
In future years Sefira was connected to the counting of the omer, a measure of barley that the Jews brought as an offering in the Holy Temple on the second day of Passover. Even as we await the rebuilding of the Third and eternal Holy Temple, we recite the blessing and fulfill the mitzva of counting the omer each evening from the second night of Passover until the eve of Shavuot. And as we do so, we, too, travel on our own personal journeys of self-refinement and purification.
This, then, is the essence of part of the uniqueness of the month of Iyar. Each day in this month has the mitzva of counting (as compared to the previous month and the next month which only have a few days with this mitzva). And each day is filled with the longing and preparation for the giving of the Torah. Similarly, each day brings with it renewed introspection and the desire for character refinement and purification.
May we complete our personal and national counting in the Holy Temple with Moshiach, immediately.