Why Do Muslims Kiss the Black Stone?
Question

Is the wisdom behind kissing the Black Stone to seek blessing (barakah) thereby?
Praise be to Allah.Shaykh Muhammad ibn ’Uthaymin (may Allah have mercy on him) said:
“The Prophet (blessings and peace of Allah be upon him) explained the wisdom behind tawaf when he said: “Circumambulation of the Ka`bah (tawaf), going between as-Safa and al-Marwah (sa‘i), and stoning the Jamarat have only been ordained to establish the remembrance of Allah.” 
The one who circumambulates the House of Allah, may He be exalted, does that while feeling awe of Allah in his heart, may He be exalted. Thus he is in a state of remembrance of Allah, may He be exalted, and all his movements – walking, kissing or touching the Black Stone and the Yemeni Corner, or pointing to the Black Stone – all come under the heading of remembering Allah, may He be exalted, because they are all acts of worship, and all acts of worship are remembrance of Allah, may He be exalted, in general terms. 
As for the words that he utters of takbهr, dhikr and du`a, they obviously come under the heading of remembering Allah, may He be exalted. 
As for kissing the Black Stone , it is an act of worship in which a person kisses a stone to which he has no connection except worshipping Allah, may He be exalted, by venerating it and following the Messenger of Allah (blessings and peace of Allah be upon him) by doing that, as it is proven that the Amهr al-Mumineهn ‘Umar ibn al-Khattab (may Allah be pleased with him) said, when he kissed the Black Stone : I know that you are a stone and have no power to harm or benefit; were it not that I saw the Prophet (blessings and peace of Allah be upon him) kissing you, I would not have kissed you.
With regard to what some ignorant people think, that the purpose behind that is to seek blessing (barakah) from it, there is no basis for that, so it is invalid.
With regard to what some heretics have said, that circumambulating the Ka`bah is like circumambulating the graves of their saints, and that it is tantamount to idolatry, this is part of their heresy. 
The believers only circumambulate the Ka`bah in compliance with the command of Allah, and whatever is done in compliance with the command of Allah, doing it is an act of worship of Allah, may He be exalted.
Do you not see that prostrating to anything other than Allah is major shirk (shirk akbar), but when Allah commanded the angels to prostrate to Adam, prostration to Adam was an act of worship to Allah, may He be exalted, and refusing to prostrate to him was an act of disbelief?
Hence circumambulation of the Kabah is one of the greatest acts of worship; it is the foundation of the Hajj, and Hajj is one of the pillars of Islam. Hence when the mataf (place of tawaf) is calm, the one who does tawaf experiences the joy of tawaf and feels in his heart that he is close to his Lord, which confirms the virtue and high status of the House of Allah. And it is Allah Whose help we seek.” (Fatawa al-‘Aqهdah, pp. 28-29)
And Allah knows best.