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Harvesting the Omer

(טו) וּסְפַרְתֶּ֤ם לָכֶם֙ מִמָּחֳרַ֣ת הַשַּׁבָּ֔ת מִיּוֹם֙ הֲבִ֣יאֲכֶ֔ם אֶת־עֹ֖מֶר הַתְּנוּפָ֑ה שֶׁ֥בַע שַׁבָּת֖וֹת תְּמִימֹ֥ת תִּהְיֶֽינָה׃ (טז) עַ֣ד מִֽמָּחֳרַ֤ת הַשַּׁבָּת֙ הַשְּׁבִיעִ֔ת תִּסְפְּר֖וּ חֲמִשִּׁ֣ים י֑וֹם וְהִקְרַבְתֶּ֛ם מִנְחָ֥ה חֲדָשָׁ֖ה לַה':

(15) You shall count for yourselves - from the morrow of the rest day, from the day when you bring the Omer of the waving - seven weeks, they shall be complete. (16) Until the morrow of the seventh week you shall count, fifty days; and you shall offer a new meal-offering to Hashem.

(ט) שִׁבְעָ֥ה שָׁבֻעֹ֖ת תִּסְפָּר־לָ֑ךְ מֵהָחֵ֤ל חֶרְמֵשׁ֙ בַּקָּמָ֔ה תָּחֵ֣ל לִסְפֹּ֔ר שִׁבְעָ֖ה שָׁבֻעֽוֹת׃ (י) וְעָשִׂ֜יתָ חַ֤ג שָׁבֻעוֹת֙ לַה' אֱלֹהֶ֔יךָ מִסַּ֛ת נִדְבַ֥ת יָדְךָ֖ אֲשֶׁ֣ר תִּתֵּ֑ן כַּאֲשֶׁ֥ר יְבָרֶכְךָ֖ ה' אֱלֹהֶֽיךָ׃

(9) You shall count seven weeks for yourselves; from when the sickle is first put to the standing crop you shall begin counting seven weeks. (10) Then you shall observe the Festival of Shavuot for Hashem, your G-d: the voluntary offerings should be commensurate with how much Hashem, your G-d, blessed you.

תניא א"ר יהודה משום ר"ע מפני מה אמרה תורה הביאו עומר בפסח מפני שהפסח זמן תבואה הוא אמר הקב"ה הביאו לפני עומר בפסח כדי שתתברך לכם תבואה שבשדות

It was taught in a baraita: "says R' Yehudah in the name of R' Akiva why did the Torah say to bring an omer measurement on Pesach? Because Pesach is the time of the (judgement for) produce the Holy One said: bring before me an omer on Pesach in order that your produce in the fields should be blessed.

אמר אביי מצוה למימני יומי ומצוה למימני שבועי רבנן דבי רב אשי מנו יומי ומנו שבועי אמימר מני יומי ולא מני שבועי אמר זכר למקדש הוא:

Abaye said it is a mitzva to count days and a mitzvah to count weeks. They rabbis of the house of Rav Ashi counted both days and weeks. Ameimar counted days, but not weeks stating that this was a "Zecher l'Mikdash"

Sefer Abudraham Hashalem p. 267
The reason God commanded to count the Omer was because each Jew was busy with their harvest and spread out in their threshing floor, so God commanded them to count, so that they would not forget the time to go up [to Jerusalem] for the festival.
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Because the world is in danger from Pesach until Shavuot in regard to the grains and in regard to the trees...therefore G-d commanded us to count these days in order that we remember the trauma of the world, so that we return to G-d with a full heart and offer supplications before G-d, that G-d will be merciful towards us and on the Creation and on the Land -- that the grain will be properly apportioned.

(ג) ... הַגָּה: ... וְנוֹהֲגִין לִשְׁטֹחַ עֲשָׂבִים בְּשָׁבוּעוֹת בְּבֵית הַכְּנֶסֶת וְהַבָּתִּים, זֵכֶר לְשִׂמְחַת מַתַּן תּוֹרָה.

(3) ... Ramah: ...We have the custom to spread out plants on Shavuot in the synagogue and in houses, as a memory for the happiness of the receiving of the Torah...."

Ben Ish Hai
The Ben Ish Hai (Rav Yosef Haim of Baghdad, 1833-1909) adds a deeper interpretation of this custom based on Kabbalistic teachings. He explains that Torah study has the effect of “Mituk Ha’dinim” – “sweetening” harsh judgments issued against a person. Even if G-d had issued a decree, Heaven forbid, against somebody, that decree can be annulled through the study of Torah. The divine Name associated with strict judgment is “Elokim,” whereas the Name associated with “Mituk Ha’dinim” is “Havaya” (Y-H-V-H). When we spell out the names of the letters of these Names (e.g. the Alef of “Elokim” is spelled out, “Alef, Lamed, Peh”), the combined numerical value of the letters of “Elokim” is 300, and the combined numerical value of the letters of “Havaya” is 72. The letter representing the number 300 is “Shin,” and the number 72 is represented by the letters “Ayin” (70) and “Bet” (2). The two letters of “Havaya,” the Ben Ish Hai explains, surround the letter of “Elokim” to neutralize its effect, such that the letter “Shin” is placed in between the “Ayin” and “Bet.” When the three letters are arranged in this fashion, they spell the word “Eseb” – “grass.” Thus, we put out vegetation on Shabuot to symbolize the profound spiritual effect of our Torah study, how it has the capacity to annul harsh judgments. As we celebrate the event of Matan Torah, we remind ourselves of how valuable and precious Torah learning is, as alluded to in the “Eseb” with which we decorate the synagogue and home.