There is a custom to spread greenery in the shul and in the home on Shavuos (Rema Orach Chaim 494). The reason for this custom is because the Medrash states that when the Jewish People received the Torah at Sinai, the mountain was originally barren and HaShem made the mountain lush with greenery. To commemorate this phenomenon, we decorate the shul and the home with greenery.
It is noteworthy that besides the reason offered by the commentators, there are three other possible reasons for this custom. One explanation is that the Gemara (Eiruvin 54a) states that the Torah is only sustained if one makes himself to be like a desert, and by seeing the greenery on Shavuos, we are inspired to be humble like Har Sinai, and then our Torah will be sustained.
Additionally, the Gemara (Shabbos 88b) states that when the Jewish People heard HaShem uttering the Ten Commandments, their souls left them, and HaShem resurrected them with the Tal of Techias Hameisim, the dew of the Resurrection. The Gemara (Sanhedrin 90b) states that the righteous will be resurrected in the future and they will be clothed, as it is said (Tehillim 72:16) viyatzitzu meiir kiesev haaretz, may [people] blossom from the city like grass of the earth. Thus, grass alludes to the idea that our souls left us and were resurrected, similar to what will occur in the future.
Lastly, the word for grass is eisev, and the letters beis and vav are interchangeable. Thus, the word eisev can be read as Esav. What is the connection between Esav and Torah? It is said (Devarim 2:3) rav lachem sov es hahar hazeh pinu lachem tzafonah, enough of your encircling this mountain; turn yourselves northward. The Medrash (Devarim Rabbah 1:19) states: if you see Esav attempting to provoke you, hide yourselves in Torah, which is referred to as tzafun, concealed. The grass, which is called eisev, alludes to Esav, as the only protection one has from Esav is to conceal himself in Torah. The grass that covers the ground reflects the Torah, which is the refuge from Esav and his overtures. Hashem should allow us to merit studying Torah with great intensity, and this Torah study will protect us from the blandishments of Esav and allow us to reach great spiritual heights.