Answer
Salam (Peace) K,
Thank you for contacting About Islam with your question.
Let us first understand what the Christians mean by the Immaculate Conception.
I have taken the definition from the following Catholic website: The Immaculate Conception
Some people think the term “Immaculate Conception” refers to Christ’s conception in Mary’s womb without the intervention of a human father; but that is the Virgin Birth.
Others think the Immaculate Conception means Mary herself was conceived by her mother “by the power of the Holy Spirit,” in the way Jesus was, but that, too, is incorrect.
The Immaculate Conception means that Mary, whose conception was brought about the normal way, was conceived without original sin or its stain—that’s what “immaculate” means: without stain.
According to Christian doctrine, the essence of original sin consists in the deprivation of sanctifying grace, and its stain is a corrupt nature.
And according to this doctrine, Mary was preserved from these defects by God’s grace; from the first instant of her existence she was in the state of sanctifying grace and was free from the corrupt nature original sin brings.
However, Muslims believe that all children come into this world without sin. But human beings, once they reach an age of understanding, have the capacity for sin. And each person will be responsible for their sins and no one else’s.
As for what Muslims believe about how Mary conceived Jesus (Peace be upon them both), this is mentioned in several places in the Quran. In fact, there is an entire chapter named after Mary (Maryam in Arabic). In this chapter, we find the story of her conception of Jesus, as follows:
{And mention, [O Muhammad], in the Book [the story of] Mary, when she withdrew from her family to a place toward the east.
And she took, in seclusion from them, a screen. Then We sent to her Our Angel, and he represented himself to her as a well-proportioned man.
She said, “Indeed, I seek refuge in the Most Merciful from you, [so leave me], if you should be fearing of Allah.”
He said, “I am only the messenger of your Lord to give you [news of] a pure boy.”
She said, “How can I have a boy while no man has touched me and I have not been unchaste?”
He said, “Thus [it will be]; your Lord says, ‘It is easy for Me, and We will make him a sign to the people and a mercy from Us. And it is a matter [already] decreed.’ “
So, she conceived him, and she withdrew with him to a remote place.
And the pains of childbirth drove her to the trunk of a palm tree. She said, “Oh, I wish I had died before this and was in oblivion, forgotten.”} (Quran 19:16-23)
I hope this helps.
Peace and please keep in touch.
Please continue feeding your curiosity, and find more info in the following links:
The Story of Maryam (Mother of Jesus)
Mary: The Honored Mother of Jesus
The Holy Spirit in Islam and Christianity