In this week's Parsha, the Torah teaches us the Mitzvah of counting the Omer, which begins on the 16th day of Nissan (the second day of Pesach) and continues until Shavuos (ויקרא כ"ג:ט"ו-ט"ז). Because the Torah there phrases a Mitzvah to count seven seeks (שבע שבתות) as well as to count fifty days (חמישים יום), we mention in our counting both the number of days and the number of weeks, as the Gemara in Menachos (דף ס"ו.) says. Rashi notes that because the Torah uses the word תמימות, complete, one must count specifically at night because that is the beginning of each new day.
What is the significance of this counting? The Sefer Rokeiach, among others, says that when Bnai Yisrael were taken out of Mitzrayim, Moshe told them that they would be receiving the Torah in 49 days from that day. In great anticipation of that day, each Jew kept for himself his own calendar of how many days remained until Mattan Torah. To commemorate this, therefore, the counting was later instituted by Hashem as a permanent Mitzvah. We start counting from Pesach, which is a celebration of the physical redemption from slavery, and continue until Shavuos, which is a celebration of the giving of the Torah, and which signified the spiritual redemption. The acceptance of the Torah and its Mitzvos is, of course, considered an even greater redemption than the physical redemption of Yetzias Mitzraim. The counting of the Omer links the two, showing that the physical redemption of Yetzias Mizraim is meaningless without the spiritual redemption of Mattan Torah.
The Midrash records that two Amoraim were once discussing this Mitzvah and one asked the other what the deeper meaning of this Mitzvah of counting is. The other Rabbi answered that at the time of Yetzias Mitzrayim, Bnai Yisrael were like a bride who was waiting to purify herself for her husband. Corresponding to the seven days that a bride must count before becoming pure, Bnai Yisrael counted seven weeks. By the time the day of Mattan Torah arrived, Bnai Yisrael were thus free from their spiritual impurity and were ready to marry themselves to Hashem at Har Sinai. Based on this, a Talmid Chacham should purify himself during these seven weeks so that he will be able to accept the Torah on Shavuos with great devotion. During these seven weeks, we are all indeed supposed to draw ourselves closer to Hashem in order to enter the holiday of Shavuos on as high a spiritual level as possible.