The accepted custom is to hang a Parochet, or curtain, outside the Aron (ark) in the synagogue. Some suggested an allusion to this practice in the verse in Bamidbar (4:6) which describes the cloth used to cover the ark when Beneh Yisrael traveled in the wilderness.
Hacham David Yosef, in his Halacha Berura, emphasizes that even if the ark itself is beautiful and ornate, it must be covered with a Parochet. He explains that the Parochet is required not for decorative purposes, but in order for the synagogue to resemble the Bet Ha’mikdash. Just as a Parochet was hung outside the Kodesh Ha’kodashim (innermost sanctum) of the Temple (where the ark was kept), similarly, we must hang a Parochet outside the Aron in the synagogue. This Halacha is mentioned by several Halachic authorities, including the Zera Emet, the Hida (in Mahazik Beracha 154:3) and Hacham Ovadia Yosef (in Yehave Da’at 6:9).
Hacham David cites the ruling of his father (Hacham Ovadia Yosef) that even if the entire congregation decides that they prefer placing the Parochet inside the ark, they may not do so. They must instead follow the universal practice of hanging the Parochet outside the ark. Hacham David adds in this context that some Sephardic congregations have the custom to hang two curtains, one inside the ark and one outside the ark, just as two curtains were hung in the Temple to separate between its two chambers. This custom is mentioned in the work Yaskil Abdi (vol. 4).
The Parochet has the Halachic status of "Tashmisheh Kedusha," a sacred article, in that it serves to cover the Aron, where the Torah is kept. As such, the Parochet may not be discarded, and must be buried along with other holy objects.
Summary: The Aron (ark) in the synagogue must be covered on the outside by a curtain, even if the Aron is itself decorative and ornate. Some congregations have the custom to hang two curtains – one inside the ark and one outside the ark. The curtain has the status of a sacred article and must therefore be buried, and not discarded.
