On Shavuot, we read the first chapter of Yechezkel, known as “Ma’aseh Merkavah” (The Divine Chariot). It describes a vision of many different kinds of angelic beings in a complicated arrangement involving color, light, and motion. Chazal called it “Mercava”, we might say, “G-d’s motorcycle”, or even, “G-d’s UFO.” The Mishna in Chagiga says that it is so esoteric is should not be studied even in small groups, yet it is the public reading for a major holiday.
Linear Annotated Translation of the Haftarah of Shavuot – where I do my best to at least describe what he was seeing, even if we cannot explain it.
As to why we read it on Shavuot – the source of the connection is in the following verses in the description of Matan Torah:
וַיִּרְאוּ אֵת אֱלֹהֵי יִשְׂרָאֵל וְתַחַת רַגְלָיו כְּמַעֲשֵׂה לִבְנַת הַסַּפִּיר וּכְעֶצֶם הַשָּׁמַיִם לָטֹהַר
They saw a vision of the G-d of Israel, and under his feet was something like transparent sapphire, like the essence of a clear sky. (Shemot 24:10)
וּמַרְאֵה כְּבוֹד ה’ כְּאֵשׁ אֹכֶלֶת בְּרֹאשׁ הָהָר לְעֵינֵי בְּנֵי יִשְׂרָאֵל
The appearance of the Kevod Hashem, was like a devouring flame at the top of the mountain, in the eyes of Bnei Yisrael.
The real question is why Yechezkel is shown this vision of Kevod Hashem as part of the prophecy of the destruction of Jerusalem.