Christians aren't the only people who believe Mary conceived Jesus when she was a virgin, Muslims also hold to the virgin birth. The Quran states in Surah 19:20-22 (Yusuf Ali Translation):
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): Thy Lord saith, 'that is easy for Me: and (We wish) to appoint him as a Sign unto men and a Mercy from Us': It is a matter (so) decreed." So she conceived him, and she retired with him to a remote place.Part of this passage closely resembles Luke 1:34, Mary said to the angel, "How can this be, since I am a virgin?"
However, it must be noted that in Christianity the virgin birth plays an infinitely greater role than it does in Islam— for contrary to the teachings of the Quran, Jesus was much more than a prophet. Muslims do not believe that Jesus is the Son of God (19:35), and consequently He cannot properly be called the Messiah (because only God Himself could fulfill the Old Testament prophecies concerning the Messiah such as that He would establish an everlasting kingdom, 2 Samuel 7:13, and bear sin, Isaiah 53). But to the Christian, Jesus is the Son of God. He is, in the fullest sense the Messiah, Immanuel, and God With Us.
For Christians, the virgin birth plays a critical role in the unwrapping of God's plan for salvation— for it was the means through which God became flesh (see Why was the Virgin Birth So Important?). It was the means through which God entered the world— fully God and fully man— so that He could die for His people. Jesus is not a sign from Allah. Rather, Jesus is God in human flesh. Jesus is the Son of God and the only way to God. Apart from Jesus, no person can be saved. Apart from Him, no man's sin can be blotted out. Apart from Jesus Christ, redemption is impossible and there can be nothing but unreasonable hope.
The Messiah that the Jews Expected and the Messiah that Came
Was the Virgin Birth Necessary? Why was the Virgin Birth So Important? (Part 1)
The Virgin Birth - Matthew 1:18
Jesus' Purpose: To Save His People From Their Sins (Part 1) - Matthew 1:21
Isaiah's Prophecy: It's Fulfillment (Part 1) - Matthew 1:22-23