The tachash first appears in the construction of the Mishkan as a skin used for the outer coverings of the Tent and for the altar and vessels on the march: the tent-covering is made of tachash skins (Shemot 26:14), and when the camp journeyed the Ark, the golden altar, and the service vessels were each wrapped in a covering of tachash skin (Bamidbar 4:6, Bamidbar 4:10, Bamidbar 4:11, Bamidbar 4:12).
The Gemara in Shabbat 28b identifies the tachash as a unique creature that existed only in Moshe's time, undetermined by the Sages whether it was a wild or a domesticated animal, bearing a single horn on its forehead, which appeared to Moshe for the moment the Mishkan was built and was then suppressed and no longer exists; from the fact that it had one horn the Gemara infers that it was a kosher species.
Shabbat 28a records a dispute underlying this: Rabbi Elazar raises the question whether the hide of a non-kosher animal can become tamei as a tent-covering, a question that in Rav Adda bar Ahava's formulation hinges on whether the tachash itself was tahor or tamei, with Rav Yosef maintaining that only the hide of a kosher animal was fit for heavenly service and so the tachash must have been kosher, while Rabbi Yehuda and Rabbi Nechemya disagree about whether there were one or two coverings.
Midrash sources elaborate on its nature: Midrash Tanchuma, Terumah 6 cites Rabbi Yehuda that it was a large kosher wild animal with one horn in its forehead and six-colored skin, from which curtains were made, while Rabbi Nechemya holds it was a miraculous creature created for the hour and hidden away the same year it was made; Kohelet Rabbah 1:9:1 likewise brings a dispute over its name and nature, with Rabbi Yochanan describing it as a kind of large animal that Hashem showed Moshe for the needs of the Mishkan and then hid away, and other opinions giving it other names (altinon, galtinon, keresh).
Bereshit Rabbah 20:12 records a related but distinct tradition about the "garments of skin" Hashem made for Adam, where the Sages debate the identity of the material (aigeya, agneya, lagai, sisarton, galei kasinon) and Rabbi Shmuel bar Nachman says it was camel-wool or rabbit-wool, showing that the sages applied similar interpretive debate to obscure skin/hide terms elsewhere in Chazal.
Among the rishonim, Rashi (Shemot 26:14) follows the Gemara's dispute between Rabbi Nechemya and Rabbi Yehuda as to whether the tachash-covering was a separate layer over the ram-skins or combined with them in a single covering half of each; the Ramban notes that over the Ark itself the techelet cloth, resembling the heavens, lay above the tachash covering, while on the other vessels the tachash covering lay uppermost; and Rabbeinu Bachya links the tachash-skin of the Mishkan to the "garments of skin" given to Adam, describing it as a wondrous skin created for its hour for the Mishkan and for covering the Ark.
Later commentators continue to discuss the practical details of these tachash coverings: Birkat Asher on Torah, Bamidbar 4:5 notes that the Ark of Testimony was covered with the parochet curtain, a covering of tachash skin, and a blue cloth, while Levush HaOrah, Bamidbar 4:10 explains, following Rashi, that the phrase "into a covering of tachash skin" used for the Ark implies a sack-like covering with an interior, whereas the other tachash coverings mentioned in the parasha were merely spread over the vessels like a cloth.
A more esoteric reading appears in Sulam on Zohar, Terumah 238, which connects the word tachash to the letters of "chash" remaining after the letter nun of "nechoshet" is removed, associating the term with a spiritual aspect of the altar rather than with a physical animal.