This question is asked by many non-Muslims and is used to hurt Muslims who do not understand this, This was an answer that I had prepared for a Christian.
He married Aisha in contract initially and then she lived with him three years later. The contract did not mean that they lived as man as wife this did not occur until after she has reached maturity.
There are varying reports about her age when she married him some sources say 6,9,12,15 and the Shia say 18. According to Sheikh Hamza Yusuf all the narrations about her age at the time of marriage are singular narrations therefore there isn't one that stands out and we can affirm that narration.
In any case when she married him, she was fully formed woman, in other words capable of child birth. This was perfectly normal in that time, as it was the practice of the Arabs at that time to marry women at 12, when they had reached puberty and they did not live together until three years after that.
In most of the books, scholars generally say the age was twelve and then she went to live with him when she was fifteen, after the emigration to Medina.
This was a normal marriage in this time because another woman Khawla said why don't you marry Aisha, this confirms it as a practice of the people.
Don’t forget that the Prophet (peace and blessings be upon him) had a dream where the angel Jibril was carrying a person and he asked who is was, the angel said it is your wife, the cloth was uncovered and it was Aisha, this happened three times. She was married to him before the Hijra to Medina and did not live with him until after which was some three years.
"But do you mean to tell me that the man who in the full flush of youthful vigour, a young man of four and twenty (24), married a woman much his senior, and remained faithful to her for six and twenty years (26), at fifty years of age when the passions are dying married for lust and sexual passion? Not thus are men's lives to be judged. And you look at the women whom he married, you will find that by every one of them an alliance was made for his people, or something was gained for his followers, or the woman was in sore need of protection." - - Dr Annie Besant (Dr Annie Besant in 'The Life and Teachings of Mohammad,' Madras, 1932)
A noted British author has observed, "No great religious leader has been so maligned as Prophet Mohammed. Attacked in the past as a heretic, an impostor, or a sensualist, it is still possible to find him referred to as "the false prophet."
A modern German writer accuses Prophet Mohammed of sensuality, surrounding himself with young women. This man was not married until he was twenty-five years of age, then he and his wife lived in happiness and fidelity for twenty-four years, until her death when he was fourty-nine. Only between the age of fifty and his death at sixty-two did Prophet Mohammed take other wives, only one of whom was a virgin, and most of them were taken for dynastic and political reasons. Certainly the Prophet's record was better than the head of the Church of England, Henry VIII." Geoffrey Parrinder, Mysticism in the World's Religions (New York: Oxford University Press, 1976, pg. 121)
Ayesha(ra) was engaged to someone else before she got engaged to Muhammad(saw):
Lady Ayesha(ra) was already engaged to a non-Muslim man named Jober Ibn Al-Moteam Ibn Oday. Back then, the people of Mecca did not object to Ayesha(ra)'s engagement to Jober because she was physically mature enough to be considered for marriage. Her parents saw that and they engaged her to Jober. It was only after this did the engagement take place, after she had already been proposed to!
In the Jewish Torah it states than any father who hasn’t married his daughter by the age of twelve, has dishonoured her. Henry the 8th wed Anne Boleyn aged twelve.
Some Hindis marry when their brides are aged twelve, the Jewish tradition has about what age a woman should be when she marries, some say 6 others say 9 and 12.
Mary mother of Jesus according to Christain sources was 12 when she gave birth to Jesus (upon them peace).
There are several reasons for this marriage, Aisha (may God be pleased with her) reported the second most narrations about him (over two thousand), she was the first female scholar and she taught hundreds if not thousands of students.
She corrected other companions when they made mistakes, she was a living authority of religious knowledge in her time. Muhammad (peace and blessing of Allah be upon him) was also married to Safiyyah, the daughter of Huyayy ibn Akhtab, the leader of a Jewish tribe in Arabia. The Prophet (peace and blessings of Allah be upon him)married her when she was 16 years old and guess what? He was her third husband; she was married twice before him.
So, how old do you think she was when she got married to her first husband? Probably around 12 or 9, just like `A’ishah (May Allah be pleased with her).
According to the Encyclopaedia Britannica—which is a Western source written by non-Muslim scholars and scientists — puberty is “in human physiology, the stage or period of life when a child transforms into an adult normally capable of procreation,” which essentially means “sexually mature.” She was engaged before him to the son of Uqbah ibn Muayt. He was one of the idol worshipers of the Quraish, who had abandoned her because of her father’s strong position in supporting Islam.
Also, when Khawlah bint Hakim suggested to him to marry Aisha, the Prophet, peace and blessings be upon him, thought thoroughly whether to accept or to refuse. He took into consideration his relation with Abu Bakr (May Allah be pleased with him).
People who try to compare one time with another really misrepresent that time.
Many people forget how amazing Aisha (may Allah be pleased with her) was, after the Prophet (peace and blessing of Allah be upon him) passed away, she did not marry again. She loved him that much that she could not bear to marry anyone else.
Thomas Hardy in the 1900's married his secretary who was 40 years his junour. So this is not unheard of in the history books.
Clint Eastword married Dina Ruiz who was 35 years younger than him. He is 79 and she is 44!
Edgar Allan Poe married his 13 year old cousin and when she died he spent the rest of his life grieving over her.
John Milton author of Paradise lost married a 16 year old.
Even Bruce Forsyth married a woman who was thirty two years his junior! So what it this then?
Also see this link about a chinese girl aged nine gave birth to a healthy child.
In Shakespeare's Romeo and Juliet, Juliet was 13 years old and Romeo was 25 so was that rape then? Was one of the greatest love stories that man ever wrote really rape? Or it something that we do not understand? And if this was wrote about then don't you think that this was very common in those days?
People who bring slander to this are really showing what they have in themselves because when a dog backs at the moon, it does not a make a difference to it.