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There is a Mitzvah to count the days and weeks from Pesach until Shavuot, and to celebrate Shavuot on the 50th day. This count establishes the date of the holiday of Shavuot.
The count starts on the eve of the second day of Pesach. We count on the eve of each day. For instance, tomorrow (Friday 2/04/21) will be the 5th day of the Omer, and we will count tonight (Thursday 1/04/21) 5 days. The counting is accompanied by a blessing.
If someone forgets to count in the evening, he can count during the entire next day until nightfall, though without making a blessing. On the next days, he continues to recite the blessing as ususal. Yet if someone forgets to count even during the next day, from the next evening and on, he can (and should) fulfill the Mitzvah of counting, but without the blessing.
This count is called the (Sfirat Haomer). What is the Omer? It is a sacrifice that was offered on the day after the First Day of Pesach. During the times of the Temple, the Offering of the Omer marked the beginning of the count to Shavuot.
One of explanations given by our Sages for this count is the following: When the Jews left from Egypt, they knew that they are about to receive the Torah and their enthusiasm led them to count the days until it arrived. On Shavuot we celebrate the Giving of the Torah. The counting reminds us that we are about to receive the Torah once again on the upcoming Shavuot and that we need to prepare for it.
Shabbat Shalom and Chag Sameach,
Arie from the Yeshiva
The blessing is (when we say the blessing, we need to know which day we are about to count):
Baruch Ata Ado-na: Elo-henu Melech haolam asher kideshanu bemitzvotav vetzivanu al sefirat aomer.
Blessed are You, Lord our God, King of the Universe, who has sanctified us with His commandments, and commanded us concerning the counting of the Omer.
We count the days:
Tonight (Thursday 1/04/21) after nightfall we say: Hayom chamishayamim laomer.
Today is (we mention here the number of days and when applicable the number of weeks) of the [count of the] Omer
After counting we say:
Harachaman hu yachazir lanu avodat bet hamikdash limkoma bim'hera veyamenu Amen Sela.
May the Merciful One restore unto us the service of the Bet Hamikdash to its place, speedily in our days; Amen, Selah