The reason why the Prophet (peace and blessings of Allah be upon him) married ‘Aa’ishah despite the age difference
Question

A Christian colleague of mine asked me why the Prophet (peace and blessings of Allah be upon him) married ‘Aa’ishah (may Allah be pleased with her) when she was nine years old and he was nearly sixty, and was he intimate with her at that age or what? In fact I do not know how to respond to that.
Praise be to Allah.The Prophet (peace and blessings of Allah be upon him) married ‘Aa’ishah (may Allah be pleased with her) after he married Sawdah bint Zam’ah (may Allah be pleased with her). She – ‘Aa’ishah – was the only virgin whom he (peace and blessings of Allah be upon him) married. And he consummated the marriage with her when she was nine years old. 
Among her virtues was the fact that the Revelation did not descend when he under one cover with any of his wives other than her. She was one of the dearest of all people to the Prophet (peace and blessings of Allah be upon him), and news of her innocence was revealed from above the seven heavens. She was one of the most knowledgeable of his wives, and one of the most knowledgeable women of the ummah as a whole. The senior companions of the Prophet (peace and blessings of Allah be upon him) used to refer to her opinion and consult her. 
With regard to the story of her marriage, the Prophet (peace and blessings of Allah be upon him) had grieved over the death of the Mother of the Believers Khadeejah, who had supported him and stood by his side, and he called the year in which she died The Year of Sorrow. Then he (peace and blessings of Allah be upon him) married Sawdah, who was an older woman and was not very beautiful; rather he married her to console her after her husband had died and she stayed among mushrik people. Four years later the Prophet (peace and blessings of Allah be upon him) married ‘Aa’ishah (may Allah be pleased with her), and he was over fifty. Perhaps the reasons for the marriage were as follows: 
1 – He saw a dream about marrying her. It is proven in al-Bukhaari from the hadeeth of ‘Aa’ishah (may Allah be pleased with her) that the Prophet (peace and blessings of Allah be upon him) said to her: “You were shown to me twice in a dream. I saw that you were wrapped in a piece of silk, and it was said, ‘This is your wife.’ I uncovered her and saw that it was you. I said, ‘If this is from Allah then it will come to pass.’” (Narrated by al-Bukhaari, no. 3682). As to whether this is a prophetic vision as it appears to be, or a regular dream that may be subject to interpretation, there was a difference of opinion among the scholars, as mentioned by al-Haafiz in Fath al-Baari, 9/181. 
2 – The characteristics of intelligence and smartness that the Prophet (peace and blessings of Allah be upon him) had noticed in ‘Aa’ishah even as a small child, so he wanted to marry her so that she would be more able than others to transmit reports of what he did and said. In fact, as stated above, she was a reference point for the Sahaabah (may Allah be pleased with them) with regard to their affairs and rulings. 
3 – The love of the Prophet (peace and blessings of Allah be upon him) for her father Abu Bakr (may Allah be pleased with him), and the persecution that Abu Bakr (may Allah be pleased with him) had suffered for the sake of the call of truth, which he bore with patience. He was the strongest of people in faith and the most sincere in certain faith, after the Prophets. 
It may be noted that among his wives were those who were young and old, the daughter of his sworn enemy, the daughter of his closest friend. One of them occupied herself with raising orphans, another distinguished herself  from others by fasting and praying qiyaam a great deal… They represented all kinds of people, through whom the Messenger of Allah (peace and blessings of Allah be upon him) was able to set out a way for the Muslims showing how to deal properly with all kinds of people. [See al-Seerah al-Nabawiyyah fi Daw’ al-Masaadir al-Asliyyah, p. 711]. 
With regard to the issue of her being young and your being confused about that, you should note that the Prophet (peace and blessings of Allah be upon him) grew up in a hot country, the Arabian Peninsula. Usually in hot countries adolescence comes early and people marry early. This is how the people of Arabia were until recently. Moreover, women vary greatly in their development and their physical readiness for marriage. 
If you think – may Allah guide you – that the Prophet (peace and blessings of Allah be upon him) did not marry any virgin other than ‘Aa’ishah (may Allah be pleased with her), and that all his other wives had been previously married, this will refute the notion spread by many hostile sources, that the basic motive behind the Prophet’s marriages was physical desire and enjoyment of women, because if that was his intention he would have chosen only those who were virgins and beautiful etc.    
Such slanders against the Prophet of Mercy (peace and blessings of Allah be upon him) by kaafirs and others of their ilk, are indicative of their inability to find fault with the law and religion that he brought from Allah, so they try to find ways to criticize Islam with regard to issues that are not related to sharee’ah. 
And Allah is the Source of strength. May Allah send blessings and peace upon our Prophet Muhammad and his family and companions. 
For more information see Zaad al-Ma’aad, 1/106.