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.

The Mishna Brura explains the custom of delaying the wearing of the Tallit, based on the following midrash on Eicha, Lamentations 2:17.

- "He carried out His decree" is interpreted as - "He tore His Royal garments". [This is the tallit.]

The word porphyra, which the midrash uses to connote "Royal garments", refers to garments dyed with purpura (Murex) snails. As a sign bemoaning the rending of the Royal garments, we delay donning the tallit, which bears strings dyed in this manner.

Rabbi Shimon Eider, in his "Summary of Halachos of the Three Weeks", explains that this midrash is also 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.