The Dome of the Rock, or Qubbat al-Sakhrah as it is known in Arabic, is one of the most misunderstood and confused buildings of the Holy Land, often believed to be the Aqsa mosque, and believed to be a mosque. Neither is correct.
The Dome of the Rock was build in 687-691 CE by the Umayyad Caliph Abd Al-Malik and his son, Al-Walid. It is believed to have been build on the place, where the Jewish Temple of Herods (the Second Temple) stood, and was meant to be a monument for this particular place, which not only is believed by Jews to have been the spot, where a lot of crucial spiritual events took place*, but also is believed by the Muslims to be the spot, where Muhammad took the first steps up to heaven on his night journey, after having traveled on the winged horse, al-Buraq, from Mecca to Jerusalem.
Exactly what the idea behind the Dome of the Rock is, is a matter of debate. Some point to the Salomonic motives inside the building as evidence that Abd Al-Malik wanted create the Third Temple, others argue that it was to be a new spiritual center for the Muslims (mostly based on letters written by his opponents), while others again see it as a reaction against Christian advances and progress in Northern Syria. The latter seems for me to be the correct assumption, since the inscriptions on the octagon inside the building carries an anti-Christian message, and the Dome of the Rock is so placed, as to challenge the Church of the Holy Sepulcher, which otherwise were the tallest building in Jerusalem at the time.
The latter is also of interest in regards of the design of the Dome of the Rock. Contrary to the Aqsa mosque, and other Islamic buildings, the Dome of the Rock is not based on Islamic architecture, but rather on Byzantine architecture, being based on an octagonal structure with a domed roof.
* Jewish tradition claims that God placed the first rock here, when He created the world, that Abraham was to sacrifice his son at this same spot, as well as a number of other events of crucial spiritual significance.