Our Parsha speaks about the Omer, and its central mitzvah: the harvest of the Omer and sacrifice of the first barley. Nowadays we only count the Omer, but when the temple stood, the Omer was a tangible thing, not just an idea.
וּסְפַרְתֶּ֤ם לָכֶם֙ מִמָּֽחֳרַ֣ת הַשַּׁבָּ֔ת מִיּוֹם֙ הֲבִ֣יאֲכֶ֔ם אֶת עֹ֖מֶר הַתְּנוּפָ֑ה שֶׁ֥בַע שַׁבָּת֖וֹת תְּמִימֹ֥ת תִּֽהְיֶֽינָה.
And you shall count for yourselves, from the morrow of the rest day from the day you bring the omer as a wave offering seven weeks; they shall be complete.
In other words, after the "rest day" we should bring the first harvest of barley that opens the harvest season together with a sacrifice :
כֶּ֣בֶשׂ תָּמִ֧ים בֶּן שְׁנָת֛וֹ לְעֹלָ֖ה לַ-ה'.
you shall offer up an unblemished lamb in its [first] year as a burnt offering to the Lord;
We then count seven weeks until the new offering of Shavuot.