Gabriel came to Mary with a message that she would give birth to Jesus. God used a young girl to bring Jesus into the world. God could have just brought a grown Jesus here in the blink of an eye. Instead He decided to use what the world thought ordinary.
Women back then had no significant role other than wife & bearing children. If their husband died they couldn't just be a single mom. They usually had to move back with their family or get remarried. They had no rights, no status in their communities. Very few women in the bible had a visit from an angel, when they did it was for an extraordinary reason. So God bringing Jesus into the world this way is pretty amazing to me.
Gabriel told Mary that Elizabeth her cousin is also having a child even though she is past childbearing age. He told Mary that nothing is impossible with God.
v. 38 (NIV) Mary responds "I am the Lord's servant, may it be to me as you have said". She first of all stated her place in God's Kingdom which we should also do. It keeps you humble and keep pride at a distance. Then she accepted her task without complaint. Her only question was "How can this be?" There is a difference between Zechariah's and Mary's responses. They both stated facts to support their confusion. I believe Zechariah questioned God and Mary honestly didn't know how it was possible. Since Zechariah was without speech and Mary had no such consequence.
What if we said the same thing as Mary any time God asks something from us? God, I am your servant. May it be to me as you have said.