Talmud Bavli, Chullin
Chullin 105a
The Talmud records that Mar Ukva would distinguish between eating meat and dairy by never eating cheese on the same day as meat, and the Sages required visible distinctions ('shinui') at the table as a safeguard against eating meat and milk together.
אָמַר מָר עוּקְבָא: אֲנָא, לְהָא מִלְּתָא, חַלָּא בַּר חַמְרָא לְגַבֵּי אַבָּא, דְּאִילּוּ אַבָּא כִּי הֲוָה אָכֵיל בִּשְׂרָא הָאִידָּנָא, לָא הֲוָה אָכֵל גְּבִינָה עַד לִמְחַר עַד הַשְׁתָּא, וְאִילּוּ אֲנָא – בְּהָא סְעוֹדְתָּא הוּא דְּלָא אָכֵילְנָא, לִסְעוֹדְתָּא אַחְרִיתָא – אָכֵילְנָא.
Mar Ukva said: I am, with regard to this matter, like vinegar, son of wine, with respect to Father, i.e., my practice is inferior to that of my father. As Father, if he were to eat meat at this time, would not eat cheese until tomorrow at this time. But as for me, only at this meal, during which I ate meat, do I not eat cheese; at a different meal on the same day I will eat cheese.
Why it matters — Foundational Talmudic discussion on why visible distinctions at the table — such as different coverings — are required between meat and dairy.