We believe the story of Adam and Eve from the Bible is true. We also have an even greater understanding of the creation and the origin of man and woman on the earth, because of modern day revelation. Modern day revelation means we have prophets who receive revelation from the Lord for us in our day, just like the prophets in the bible did in their day.
You can find out more here -
Agency and the Fall of Adam and Eve
or here -
LDS.org - Topic Definition - Creation