If you want to know more about Mormonism, have a look at the South Park parody.
Basically, Mormons believe that a guy named Joseph Smith heard that Jesus had lived in America. Smith 'wrote down' information he found on golden plates when an angel directed him to a box of plates. This information became the Book of Mormon that's read alongside the Bible.
If you've never encountered them in your city, you're lucky. They missionize a lot overseas, it's usually two young guys in a suit approaching you in the street and talking for a long time. Mormons have a low social status in Europe and are mostly seen as a Christian sect/outcasts.