Hz Maryam bint-Imran (AS) or The Virgin Mary, the mother of Jesus (AS), holds an exalted position in the history of Islam. She is the only woman mentioned by name in The Quran, and there is an entire chapter, Surah Maryam, named after her.
In Surah al-Imran, Allah says: 
Behold! the angels said: “O Mary! Allah has chosen you and purified you, chosen you above the women of all nations.”
Also, Prophet Muhammad (PBUH) described her as one of the most “perfect” women in the history of humanity. Narrated by Abu Musa al-Ash’ari (RA): 
Allah’s Apostle (PBUH) said, “Many amongst men attained perfection but amongst women none attained perfection except Mary the daughter of Imran, and Asiya the wife of Pharaoh.”
Hz Maryam (AS) belonged to the family of Imran. Her Mother prayed to Allah for a child. When her mother conceived, she vowed to Allah to dedicate her unborn child to His service, free from all worldly affairs. She also prayed for her child to be protected from the “touch” of Satan. Allah accepted her prayer and described it in these verses of Surah al-Imran: 
When wife of Imran said: “My Lord! surely I vow to You what is in my womb, to be devoted (to Your Service); accept therefore from me, surely You are the Hearing, the Knowing.”
And when she was delivered she said: “My Lord! Lo! I am delivered of a female — Allah knew best of what she was delivered — the male is not as the female; and lo! I have named her Mary, and lo! I crave Your Protection for her and for her offspring from Satan the outcast.”
Allah accepted Hz Maryam (AS) into His service, and chose Hz Zachariah (AS) to be her guardian. He was chosen out of all of the scribes of his time, who were gathered together and instructed to throw their pens into a stream. They were told that whoever’s pen flowed against the current would be the child’s guardian. Zachariah (AS)’s pen was the one that went against the current.
According to the Quran, whenever Hz Zachariah went to visit Hz Maryam (AS), he found her with food and supplies and he wondered about its source and asked her about it, to which she used to respond that the food came from Allah. The Quran confirms this through the following verse: 
And We made Zachariah her guardian. Whenever Zachariah went into the sanctuary where she was, he found that she had food. He said: “O Mary! From where comes to you this (food)?” She answered: “It is from Allah. Allah gives without measure to whom He wills.”
She grew up as a righteous, pure, and pious Muslim woman worshipping Allah. Hz Maryam (AS) secluded herself from her family. She retired to the eastern side of the Sacred Masjid in Jerusalem where she prayed. It was in this state that an angel appeared to her in the shape of a man. As she thought the angel was a man, she was frightened and asked him not to invade her privacy. 
And make mention of Mary in the Scripture, when she had withdrawn from her people to a chamber looking East, and had chosen seclusion from them. Then We sent to her Our Spirit (angel) and it assumed for her the likeness of a perfect man.
She said: “Lo! I seek refuge in the Beneficent One from you, if you are Allah-fearing.”
He said: “I am only a messenger of your Lord, that I may bestow on you a faultless son.”
She said: “How shall I have a son, seeing that no man has touched me, and I am not unchaste?”
He said: “So (it will be). Your Lord says: ‘It is easy for Me. And (it will be) that We may make of him a revelation for mankind and a mercy from Us, and it is a thing ordained.'”
So she conceived him, and she retired with him to a remote place. And the pains of childbirth drove her to the trunk of the palm-tree.
She said: “Oh, would that I had died before this and had become a thing of naught, forgotten!”
Then (one) cried to her from below her, saying: “Grieve not! Your Lord has placed a stream beneath you, and shake the trunk of the palm-tree toward you, you will cause ripe dates to fall upon you. So eat and drink and be consoled. And if you meet any mortal, say: ‘Lo! I have vowed a fast to the Beneficent, and may not speak this day to any mortal.'”
Then she brought him to her own folk, carrying him.
They said: “O Mary! Thou have come with an amazing thing. O sister of Aaron! Your father was not a man of evil nor was thy mother unchaste.”
Then she pointed to him. They said: “How can we talk to one who is in the cradle, a young boy?”
He said: “I am indeed a servant of Allah: He has given me revelation and made me a prophet; and has made me blessed wheresoever I may be, and has enjoined upon me prayer and almsgiving so long as I remain alive, and (has made me) dutiful toward her who bore me, and has not made me arrogant, unblest. Peace on me the day I was born, and the day I die, and the day I shall be raised alive!”
Such was Jesus, son of Mary: (this is) a statement of the truth concerning which they doubt.
Just as Allah created Hz Adam (AS), without a male or female parent, He created Hz Jesus (AS) to be born from a female without a male, as a sign for humankind. 
Indeed, Jesus is like Adam in front of Allah. He created him from dust, then said to him, ‘Be’ and he was.
The Quran upholds the example of Hz Maryam (AS) as a pious and chaste woman: 
And Mary, daughter of Imran, who guarded her chastity, therefore We breathed therein something of Our Spirit. And she put faith in the words of her Lord and His scriptures, and was of the obedient.
Also, when naming the best woman who ever lived, Prophet Muhammad (PBUH) named Hz Maryam (AS).
Narrated by Ali (RA): 
The Prophet (PBUH) said, “The best of the world’s women is Mary (at her lifetime).”
- The Quran 03:42 (Surah al-Imran)
- Sahih Bukhari Volume 5, Book 57, Number 113
- The Quran 03:35-37 (Surah al-Imran)
- The Quran 03:37 (Surah al-Imran)
- The Quran 19:16-34 (Surah Maryam)
- The Quran 03:59 (Surah al-Imran)
- The Quran 66:12 (Surah at-Tahrim)
- Sahih Bukhari Volume 5, Book 58, Number 163