Our sages tell us that the holiday of Passover was given to the Jewish people as a gift from Hashem. We, as a people, had descended to the 49th level of impurity in Egypt. We were on the brink of plunging to the 50th level of impurity, the point of no return, when Hashem in His infinite mercy, quickly redeemed us from the Land of Egypt. As an expression of gratitude to Hashem, we count the days between Passover and Shavuot as a way of lifting ourselves up from the depths of the impurity of Egypt to the heights of purity experienced at Mount Sinai. However, there is another reason why we count the Omer.
All Biblical holidays have a specific date mentioned by the Torah except for Shavuot.
The holiday of Passover is on the 15th day of the 1st month, Rosh Hashanah is on the 1st day of the 7th month, Yom Kippur is the 10th day of the 7th month, Sukkot is the 15th Day of the 7th month, and Shmeni Atzeret is the 22 day of the 7th month. However there is no mention of a date for the holiday of Shavuot. The Torah is sending us a message. Even though the Torah was given close to 3500 years ago when our ancestors stood at Mount Sinai , the Torah should not be seen as some old, out of date, antiquated object. Rather we count the days to the holiday of Shavuot with great anticipation, looking foward to marking the day when Hashem gave the Jewish people 613 beautiful gifts, good at any time in every generation.