What's in a name? The Torah (Shemos 16:36) tells is that an omer is a tenth of an ephah (a dry measure). Rashi on this verse makes a calculation and informs us that a tenth of an ephah is the minimum amount of dough needed for the requirements of taking challah and for the menachos. What is of special noteworthiness is that the Torah and the rabbis take note of this weight measurement of omer and refer both to the korban of barley that is brought on the second day of Pesach (the sixteenth of Nissan) not as the offering of barley but as the korban omer (Vayikra 23:10, 11, 12). Moreover, the mitzvah of counting and connecting the yom tov of Pesach with that of Shavuos is called counting the omer (Sefer HaChinuch, mitzvah 306). Why stress the omer in each case, when even regarding the korban tamid, brought twice daily, the Torah ordains (Bamidbar 28:5) that it be accompanied by a tenth ephah of fine flour as a meal offering, with no mention of the omer?
Rav Yosef Salant zt"l in his Be'er Yosef suggests a fascinating answer. He notes that the first time the term omer is used in the Torah is in conjunction with the mann that miraculously sustained the Jewish nation in the desert for forty years. Moshe directs them to (Shemos 16:16) "gather from it an omer per person." Moreover, when Moshe is told to hide and preserve some mann so that future generations will be able to actually witness the miracle food, he places an omer's worth of mann for safekeeping in the aron (Yuma 52b). The gemarah (Kiddushin 38a) teaches that the mann stopped falling on the seventh of Adar - the day of Moshe's death - as the mann fell in his honor. Unlike the other times that the Torah teaches (Shemos 16:20) that that which was left overnight became worm infested and putrid, here it lasted until they crossed the Jordan, until the sixteenth of Nissan. From then on they ate of the produce of the land.
It is thus no coincidence that the Torah ordained that the korban omer whose purpose is to thank Hashem for His kindness in renewing the harvest (and we thus present Him with this produce prior to our benefiting from it - Sefer HaChinuch mitzvah 306) was to be brought on the day the mann stopped nourishing us. Thus, the sixteenth of Nissan, the second day of Pesach, is the day the korban omer was brought.
Our bringing the korban omer results in our remembering the omer of the mann. As the mann was hamotzi lechem min hashomayim - the produce of Eretz Yisroel is hamotzi lechem min haaretz. The motzi is the same. The produce of the Land of Israel represented by the omer of barley is no less a divine blessing than the omer of mann.
Rav Menachem Mendel of Rimanov suggests a novel interpretation to the name mann. When the mann descended the Jewish nation did not know what it was (Shemos 16:15), referring to the new found object they said to one another "mann hu". Rav Menachem Mendel learns "mann hu" as referring not only to the object of the mann, but additionally to the persons who ate the mann as they were constantly being elevated and spiritually uplifted by this divine nourishment. "Mann hu" - they didn't recognize each other and the positive transformation it had on the people.
Our counting the omer from Pesach to Shavuos is likewise to remind us of the special nourishing food for thought the mann provided. There is no room for jealousy or envy if one believes their sustenance is being provided by Hashem. Ben Azzai taught (Yuma 38a) "by your name shall they call you, and in your place shall the seat you, and from your own position shall they provide you." Rashi explains that each person's livelihood (parnasah) is not a gift of others good will, rather it is the personalized parnasah that Hashem has allotted to him.
We count the omer until Shavuos, out time of reaccepting the Torah and our commitment towards renewed Torah study, as the omer itself served in that capacity. The omer of mann that Moshe hid was removed from its case many hundreds of years later by Yirmiyahu Hanavi. In response to the excuse of the Jewish people for not studying Torah - that they needed to earn a livelihood - Yirmiyahu said learn from the omer of mann -as He sustained them with a minimum effort and exertion so will he provide for you.
The omer teaches: you make time for Him, He'll make time for you.