Many communities have a custom to consume sheep for the Shabbat of Parshat Yitro. Why is this done?
This is related etymologically by R' Hirsch: The giving of the Torah is referred to as מטן תורה, mutton torah. As such, it is proper to consume mutton on the Shabbat of Parshat Yitro. It is also permitted to do so on Shavuot, however it is customary instead to eat sheep's cheese, as we do not eat meat then. Bedieved, when no mutton is available, one may consume lamb, as it would be mutton the next year.
When the Jews left Egypt, a land where sheep were worshiped as deities, they needed seven weeks to leave behind the vestiges of sheep-worhip and prepare themselves to receive the Torah and become God's nation as described in parashas Yisro. Therefore, when God appeared to them and presented them with the Decalogue, He included a reference to how far they had come, how much they had grown. He said (20:2–5,in loose translation):
אָנֹכִי ה׳ אֱלֹקֶיךָ אֲשֶׁר הוֹצֵאתִיךָ מֵאֶרֶץ מִצְרַיִם מִבֵּית עֲבָדִים. לֹא יִהְיֶה לְךָ אֱלֹהִים אֲחֵרִים עַל פָּנָי. לֹא תַעֲשֶׂה לְךָ פֶסֶל וְכָל תְּמוּנָה אֲשֶׁר בַּשָּׁמַיִם מִמַּעַל וַאֲשֶׁר בָּאָרֶץ מִתָּחַת וַאֲשֶׁר בַּמַּיִם מִתַּחַת לָאָרֶץ. לֹא תִשְׁתַּחֲוֶה לָהֶם וְלֹא תָעָבְדֵם
I am God, your god, who has taken you out of Egypt, the place of worshipers. You're not going to have any other gods along with me. You're not going to make a graven image of — baa — heavens or of — baa — earth or of — baa — water. You won't bow to them or worship them.
To commemorate this event, we have a custom to eat sheep the week of parashas Yisro.