This marble structure is the mihrab of the Qibly mosque which is at the front of Masjid al-Aqsa. The mimbar (pulpit) on the right was donated by the Jordanian government after the original (which was a gift from Salahuddin Ayyubi) was destroyed in a fire started by a fanatical zionist in 1969.
Masjid al-Aqsa is the second house of Allah created on earth: Abu Dharr (may Allah be pleased with him) reported that he asked the Prophet (peace and blessings of Allah be on him), “O Prophet of Allah, which Masjid was built first on earth?” The Prophet (peace and blessings of Allah be on him) replied, “The Sacred Masjid of Makkah”. Abu Dharr (may Allah be pleased with him) again asked, “Which was next?” The Prophet (peace and blessings of Allah be on him) said, “The Masjid al-Aqsa”. Abu Dharr (may Allah be pleased with him) further asked “How long was the period between the building of the two Masajid?” The Prophet (peace and blessings of Allah be on him) said, “Forty years. Apart from these, offer your prayers anywhere when it is time to pray, although excellence is in praying in these Masajid”. [Sahih al-Bhukari]
When the Crusaders captured Jerusalem in 1099 CE, Masjid al-Aqsa was desecrated. Pigs were installed in the mihrab and a church was erected in place of one of it’s oratories. Imad Eddin (Salahuddin’s biographer) speaks of the mihrab of the mosque being full of pigs and excrement.
In around 1119 CE, King Baldwin II of Jerusalem granted one wing to the newly formed Knights Templar order and the building became their headquarters.
The original mimbar, considered one of the most beautiful in the world, was made of over 10,000 interlocking pieces of Cedar and other wood, ivory and mother of pearl affixed without a drop of glue or a single nail. After the reconquest of Jerusalem Masjid al-Aqsa was filled for Jumma prayers for the first time in 88 years, people wept with emotion as the Qadi of Jerusalem, Muhyi ad-Din al-Qurashi mounted the new pulpit.
References: AtlasTours.com, Wikipedia, A history of Jerusalem – Karen Armstrong, The Crusades – S.E. Al-Djazairi