When Mormons speak of "God," they are referring to Heavenly Father or God the Father, the first member of the Godhead.
According to the Mormon scriptures, God the Father and Jesus Christ appeared together to 14-year-old Joseph Smith, the founder of Mormonism, telling him that all Christian denominations that existed at that time were wrong. This teaching is the theological foundation of the LDS church.
Heavenly Father is equated with Elohim in the Old Testament (whereas Jesus Christ is identified with Jehovah).
Mormons regard God (i.e. "Heavenly Father") as the all-powerful, all-good ruler of the universe who also loves and cares for humans. There is no other being in the universe, including Satan, that rivals his ability or is a true threat to his reign.
Mormons believe God has a physical body. This belief is based on particular biblical passages - such as those in which Moses speaks to God "face to face" (cf. Exod. 33) or Stephen sees Jesus standing at the right "hand" of God (cf. Acts 7) - as well as divine revelation to Joseph Smith.
An important part of heavenly father's work in LDS theology is that "he is the Father of our spirits." God is the celestial father of spirit children, who exist on earth now as flesh-and-blood human beings.