I need to know why is Ka'ba covered with black cloth?

All perfect praise be to Allaah, The Lord of the Worlds.  I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.

Draping the Ka'bah with black cloth has no religious significance, as far as we know. The first one to cover it with black cloth was the Abbasid Caliph An-Naasir and then it came to be covered likewise until our present day. Before that, it was covered with white, red, or other colors.

Al-Bujayrimi in his book about the history of Ka'bah, wrote, "The tribe of Quraysh used to share the privilege of draping the Ka'bah until Abu Rabee'ab ibn al-Mugheerah came and said to the Quraysh, ‘I will take the responsibility of draping the Ka'bah on my own for one year and the entire Quraysh combined would do it for the other year.'"

It was also said that he used to contribute towards half of the draping expenses every year and continued to do so until his death. Due to this, the Quraysh nicknamed him Al-'Adl ("the Equivalent") as he equaled the whole tribe of Quraysh in terms of contributing towards the expenses of draping the Ka'bah. His children also came to be called "the sons of Al-'Adl. His drape was not removed when the time of draping came; instead, a new drape was put over it – a practice which continued till the coming of the Prophet Muhammad . Abu Bakr, 'Umar and 'Uthmaan all, draped it with Qibatiyyah, (a kind of silk), Mu'aawiyah draped it with silk brocade, Qibatiyyah and Hibarah (a certain kind of wrap or veil).

It was also wrapped with silk brocade on the day of Aashooraa' (the tenth of Muharram, the first month in the Islamic calendar) and with Qibatiyyah at the end of Ramadan. Al-Ma'moon draped it with red brocade, white brocade and Qibatiyyah cloth. Thus it came to be called "the Red" on the Day of Tarwiyah (the eighth day of Thul-Hijjah, during the Hajj), "the Qibatiyyah" on the first day of the month of Rajab (the seventh month in the Islamic calendar), and "the White Brocade" on the twenty-seventh of Ramadan.

Some said that it was thus draped during the reign of the Abbasid Caliph, Al-Mutawakkil, then during the reign of An-Naasir it was draped with black silk, which continued every year up to this day. The cloth used in draping the Ka'bah is brought from two villages in Cairo, namely Basoos and Sindabees, which were endowed by King As-Saalih Ismaa'eel ibn An-Naasir Muhammad ibn Qalaawoon around 750 CE. Today, they are more than two villages.

To sum up, the preponderant opinion is that the first person to ever drape the Ka'bah was Tubba' Al-Himyari. This was about nine hundred years before the advent of Islam. It was also said that the first to wrap it with brocade was Abdul-Malik ibn Marwaan, and this is what is meant by saying that it was first wrapped with brocade by Al-Hajjaaj, for the latter was a governor during the reign of Abdul-Malik.

Imaam Al-Balqini was once asked whether it was permissible to wrap the Ka'bah with silk embroidered with gold, and whether it was permissible to carry this drape and display it in the streets for people to see it (as was the custom). He answered in the affirmative and said, "Yes, since to do so is a matter of veneration for the Ka'bah, which may incur reward and favor both in this life and the Hereafter. And it is permissible to display it on the streets with it (to show it to people) since doing so involves proper consecrating for a sacred object." [As-Seerah Al-Halabiyah]

Allaah Knows best.