The Shulchan Aruch (555:1) states:
It is customary not to lay Tefillin on Tisha b’Av at Shacharit, and not a Tallit. Rather, one should wear a Tallit Katan beneath his clothes, without a blessing. And at Mincha, we put on Tzitizit and Tefillin, with the blessings.
According to the Mishnah Brurah the custom of delaying the wearing of the Tallit, is based on a midrash regarding the following passage in Eicha, Lamentations 2:17.
(עָשָׂה ה’ אֲשֶׁר זָמָם בִּצַּע אֶמְרָתוֹ אֲשֶׁר צִוָּה מִימֵי קֶדֶם הָרַס וְלֹא חָמָל וַיְשַׂמַּח עָלַיִךְ אוֹיֵב הֵרִים קֶרֶן צָרָיִךְ (איכה ב’:י”ז
“The Lord has done that which He devised; He has carried out His decree which He commanded from days of old; He has destroyed unsparingly; He has caused the enemy to rejoice over you; He has exalted the horn of your adversaries.”
Rabbi Yaakov of Kfar Chanan explains – בִּצַּע אֶמְרָתוֹ – “He has carried out His decree” as – בזע פרפורין שלו – “He has torn His porphyra”.
Porphyra refers to the woolen cloth dyed with purpura (Murex) snails, which was reserved for use by royalty. In this midrash, Rabbi Yaakov depicts the rending of the “Royal Garments” as part of the destruction wrought by G-d on His people. (Note the similarity of the word אמרתו and the Aramaic word for a bordered garment – אימרה.)
To bemoan the rending of the Royal Garments, we delay donning the tallit, which bears woolen strings dyed from purpura. Rav Moshe Isserles notes (הגהות מיימוניות הלכות תעניות פרק ה הלכה יא) that this common practice among the Jews of Ashkenaz is associated with the homiletic interpretation of the passage.
In addition, Rabbi Shimon Eider, in his “Summary of Halachos of the Three Weeks”, cites this midrash as the source of the halacha to remove the parochet (curtain) from the Aron Kodesh (Torah ark) on the eve of Tisha b’Av. The torn “Royal Garments” dyed from purpura are a reference to the parochet of the Beit HaMikdash partitioning off the Holy of Holies. This curtain, which was made from fine textiles including those dyed with purpura, was brazenly pierced by Titus.
In The Wars of the Jews (Book V, Chapter V), Josephus (who was a cohen) describes the parochet at the time of Second Temple:
It was a Babylonian curtain, embroidered with blue, and fine linen, and scarlet, and purple, and of a contexture that was truly wonderful. Nor was this mixture of colours without its mystical interpretation, but was a kind of image of the universe; for by the scarlet there seemed to be enigmatically signified fire, by the fine flax the earth, by the blue the air, and by the purple the sea.
May we continue to merit the rebuilding of all that has been destroyed.