Why do Prophet, sallallaahu alayhi wa sallam, kissed the black stone during Tawaaf?

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 as well as that of his family and all his companions.

It is confirmed that the Prophet used to kiss the Black Stone. 'Umar came to the Black Stone, kissed it and said: "I know for sure that you are a stone which can neither harm nor benefit, and had I not seen the Prophet kissing you, I would not have kissed you." [Al-Bukhari and Muslim]

Ibn Hajar said: "The statement of 'Umar proves that one should submit himself to Allaah in matters of religion and strictly abide by it even if its wisdom is not known. This is a great fundamental in following the Prophet in whatever he did even if one does not know the wisdom of such an act of worship."

The Prophet kissed the Black Stone by an order from Allaah. Indeed all the acts of worship that the Prophet did, and his narrations are from revelation by Allaah, as Allaah Says about him (what means): {Nor does he speak of (his own) desire. It is only a Revelation revealed.}[Quran 53:3-4]

Therefore, a Muslim should submit himself to the commandments of Allaah and to the orders of the Prophet even if he does not know the wisdom thereof. 

Allaah Knows best.