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The Ka'aba (الكعبة, lit. "the Cube") is the holiest mosque in Islam located in Mecca (Muhammad's city of birth) and is figuratively known as the "House of God" (or Bayt Allah, lit. "House of Allah"). Another name for the Ka'aba is Masjid al-Haram, which means "Mosque of the sanctuary", where "the sanctuary" is the name for the part of the city of Mecca that is considered sanctified.
Origins and ritual significance
Prior to Muhammad claiming to receive revelations from Allah, the Ka'aba served as a popular pagan shrine that housed 360 idols and images of mostly pagan deities and attracted pilgrims and trade from many parts of Arabia. Particularly emphasized at this shrine during Muhammad's pre-Islamic years was the worship of the pagan Arab god Hubal, often symbolically affiliated with the crescent moon symbol.
Islamic scriptures teach that Abraham (Ibrahim) built the Ka'aba with Ishmael around the time he "binded" Ishmael (a legend inspired by, though slightly different from, the Binding of Isaac).
Qibla, or direction of prayer
Muslims worldwide face the Ka'aba in Mecca five times a day to preform their daily prayers (another of the Five Pillars of Islam). In this capacity, as the direction of prayer, the Ka'aba is referred to as the Qibla. While it is taught by orthodox Islam that the Qibla changed during Muhammad's lifetime from Jerusalem to the Ka'aba, some recent critical scholarship has suggested that early Muslims after Muhammad's death used to face the city of Petra for several decades. While critical research on the history of the Qibla has not yet proven entirely conclusive or achieved universal acceptance amongst scholars, these findings do cast a good deal of doubt on the orthodox belief in the finalization of the Qibla at the Ka'aba in Mecca during Muhammad's lifetime.
Today, as with many Arabs during the pre-Islamic period, Muslims travel to the Ka'aba to perform the Hajj ceremony (which reflects in great detail the pilgrimage rituals of the pre-Islamic Arabs) at least once during their lifetime if they are financially and physically able.The Hajj is one of Islam's Five Pillars and has its rituals outlined in some detail in the Qur'an.
Housed in the eastern corner of the Ka'aba's walls is the black stone, which is known to have been a sacred baetyl revered by the pre-Islamic Arabs. Islamic scriptures teach that the stone fell from heaven and was once completely white, only to be lost during Noah's flood and blackened by the sins of mankind. This stone is then said to have been provided back to Ibrahim by Gabriel as Ibrahim was constructing the Ka'aba
According to historians
The above view is outlined by Crone as a possibility among others (see also: Hubal).
Islamic scriptures state that the original Ka'aba built by Abraham was rather more rectangular than cubic, but that due to reconstruction the Ka'aba had lost its original dimensions. The story recorded suggests that the Ka'aba, when Muhammad was growing up, used to be rectangular in shape but that a natural disaster decimated the structure such that it had to be rebuilt. The Quraysh, revering this structure, are said to have lacked sufficient "clean money" (that is, money untainted by sinful business, such as gambling and prostitution), and thus were only able to rebuild the temple in the shape of a cube. It is thus suggested that the short, semi-circular wall opposite the Iraqi (northwestern) wall of the Ka'aba delineates the portion of earth which in fact, counts as a part of the Ka'aba itself, despite its falling beyond the Ka'aba's walls. Consequently, pilgrims circumambulating the Ka'aba are able to earn the blessing of having "entered it" without having to step inside.
The Ka'aba has been destroyed deliberately and by natural disasters and thus reconstructed several times over since the seventh century. 
The following verses describe the origins of the Ka'aba
Note that "Becca" here is said to refer to Mecca, although some critical scholars have suggested that the word is simply a typographical error or misspelling.
97. Wherein are plain memorials (of Allah's guidance); the place where Abraham stood up to pray; and whosoever entereth it is safe. And pilgrimage to the House is a duty unto Allah for mankind, for him who can find a way thither. As for him who disbelieveth, (let him know that) lo! Allah is Independent of (all) creatures.
126. And when Abraham prayed: My Lord! Make this a region of security and bestow upon its people fruits, such of them as believe in Allah and the Last Day, He answered: As for him who disbelieveth, I shall leave him in contentment for a while, then I shall compel him to the doom of Fire - a hapless journey's end!
127. And when Abraham and Ishmael were raising the foundations of the House, (Abraham prayed): Our Lord! Accept from us (this duty). Lo! Thou, only Thou, art the Hearer, the Knower.
128. Our Lord! And make us submissive unto Thee and of our seed a nation submissive unto Thee, and show us our ways of worship, and relent toward us. Lo! Thou, only Thou, art the Relenting, the Merciful.129. Our Lord! And raise up in their midst a messenger from among them who shall recite unto them Thy revelations, and shall instruct them in the Scripture and in wisdom and shall make them grow. Lo! Thou, only Thou, art the Mighty, Wise.
The following verse suggests that fighting should not take place around the Ka'aba unless it is instigated
The following verses describe the Qibla, or direction of prayer, as having shifted to the Ka'aba and further argue that the Jews and Christians (referred to in Islam as the People of the Book) of Muhammad's time knew of the Ka'aba (presumably as having Abrahamic rather than pagan origin) "like they knew their sons" (i.e. "like the back of their hands")
Note that "the inviolable place of worship" here is Pickthall's translation of Masjid al-Haram (one of the names of the Ka'aba) which can mean both the "Mosque of the sanctuary" as well as the "the sanctified mosque"
145. And even if thou broughtest unto those who have received the Scripture all kinds of portents, they would not follow thy qiblah, nor canst thou be a follower of their qiblah; nor are some of them followers of the qiblah of others. And if thou shouldst follow their desires after the knowledge which hath come unto thee, then surely wert thou of the evil-doers.
146. Those unto whom We gave the Scripture recognise (this revelation) as they recognise their sons. But lo! a party of them knowingly conceal the truth.
147. It is the Truth from thy Lord (O Muhammad), so be not thou of those who waver.
148. And each one hath a goal toward which he turneth; so vie with one another in good works. Wheresoever ye may be, Allah will bring you all together. Lo! Allah is Able to do all things.
149. And whensoever thou comest forth (for prayer, O Muhammad) turn thy face toward the Inviolable Place of Worship [the Ka'aba]. Lo! it is the Truth from thy Lord. Allah is not unaware of what ye do.150. Whensoever thou comest forth turn thy face toward the Inviolable Place of Worship [the Ka'aba]; and wheresoever ye may be (O Muslims) turn your faces toward it (when ye pray) so that men may have no argument against you, save such of them as do injustice - Fear them not, but fear Me! - and so that I may complete My grace upon you, and that ye may be guided.