Thank you for this very good question. It seems only fitting to answer your question by giving you verses from the Quraan. The following verses show the Islaamic belief of Mary’s birth, her high status among all women, the virgin birth of her son Jesus, peace be upon him, and a few additional verses from his life.
Birth of Mary
(Remember) when the wife of 'Imrân said: “O my Lord! I have vowed to You what (the child that) is in my womb to be dedicated for Your services (free from all worldly work; to serve Your Place of worship), so accept this, from me. Verily, You are the All-Hearer, the All-Knowing.” Then when she delivered her [child Maryam (Mary)], she said: “O my Lord! I have delivered a female child,” - and Allâh knew better what she delivered, - “And the male is not like the female, and I have named her Maryam (Mary), and I seek refuge with You (Allâh) for her and for her offspring from Shaitan (Satan), the outcast.” So her Lord (Allâh) accepted her with goodly acceptance. He made her grow in a good manner and put her under the care of Zakariyâ (Zachariya). Every time he entered Al-Mihrâb to (visit) her , he found her supplied with sustenance. He said: “O Maryam (Mary)! From where have you got this?” She said, “This is from Allâh.” Verily, Allâh provides sustenance to whom He wills, without limit." (Aali Imran 3:35-37)
At that time Zakariyâ (Zachariya) invoked his Lord, saying: “O my Lord! Grant me from You, a good offspring. You are indeed the All-Hearer of invocation.” Then the angels called him, while he was standing in prayer in Al-Mihrâb (a praying place or a private room), (saying): “Allâh gives you glad tidings of Yahya (John), confirming (believing in) the Word from Allâh *, noble, keeping away from sexual relations with women, a Prophet, from among the righteous.” He said: “O my Lord! How can I have a son when I am very old, and my wife is barren?” Allâh said: “Thus Allâh does what He wills.” He said: “O my Lord! Make a sign for me.” Allâh said: “Your sign is that you shall not speak to mankind for three days except with signals. And remember your Lord much (by praising Him again and again), and glorify (Him) in the afternoon and in the morning.” And (remember) when the angels said: “O Maryam (Mary)! Verily, Allâh has chosen you, purified you (from polytheism and disbelief), and chosen you above the women of the 'Alamîn (mankind and jinns) (of her lifetime).” O Mary! “Submit yourself with obedience to your Lord (Allâh, by worshipping none but Him Alone) and prostrate yourself, and Irkâ’i (bow down etc.) along with Ar-Râki’ûn (those who bow down etc.).” (Aali Imran 3:38-43)
(Remember) when the angels said: “O Maryam (Mary)! Verily, Allâh gives you the glad tidings of a Word “Be!” - and he was! i.e. 'Iesa (Jesus) the son of Maryam (Mary)] from Him, his name will be the Messiah 'Iesa (Jesus), the son of Maryam (Mary), held in honour in this world and in the Hereafter, and will be one of those who are near to Allâh.” “He will speak to the people in the cradle and in manhood, and he will be one of the righteous.” She said: “O my Lord! How shall I have a son when no man has touched me.” He said: "So (it will be) for Allâh creates what He wills. When He has decreed something, He says to it only: “Be!” and it is. And He (Allâh) will teach him 'Iesa (Jesus)] the Book and Al-Hikmah (i.e. the Sunnah, the faultless speech of the Prophets, wisdom, etc.), (and) the Taurât (Torah) and the Injeel (Gospel). And will make him 'Iesa (Jesus)] a Messenger to the Children of Israel (saying): "I have come to you with a sign from your Lord, that I design for you out of clay, as it were, the figure of a bird, and breathe into it, and it becomes a bird by Allâh’s Leave; and I heal him who was born blind, and the leper, and I bring the dead to life by Allâh’s Leave. And I inform you of what you eat, and what you store in your houses. Surely, therein is a sign for you, if you believe. And I have come confirming that which was before me of the Taurât (Torah), and to make lawful to you part of what was forbidden to you, and I have come to you with a proof from your Lord. So fear Allâh and obey me. Truly! Allâh is my Lord and your Lord, so worship Him (Alone). This is the Straight Path. Then when 'Iesa (Jesus) came to know of their disbelief, he said: “Who will be my helpers in Allâh’s Cause?” Al-Hawâriûn (the disciples) said: “We are the helpers of Allâh; we believe in Allâh, and bear witness that we are Muslims (i.e. we submit to Allâh).” Our Lord! We believe in what You have sent down, and we follow the Messenger 'Iesa (Jesus)]; so write us down among those who bear witness (to the truth i.e. Lâ ilâha ill-Allâh - none has the right to be worshipped but Allâh). (Aali Imran 3:45-53)*