Heavenly Father in Mormonism
One of the most common titles of God in LDS theology, which is also an affectionate address uttered by Mormons, is "heavenly Father." Heavenly father is an important figure in LDS history, as both he and Jesus Christ appeared to fourteen-year-old Joseph Smith, the founder of Mormonism (depiction to the right; one of the most common images in Mormonism), telling him that all Christian denominations that existed at that time were wrong (e.g. Roman Catholicism and mainline Protestant denominations). This teaching is the theological foundation of the LDS church.
In Mormon belief, the LDS church represents the "restoration" of the New Testament church, founded by Christ and the Apostles in the first century. Therefore, it is important to understand the differences between LDS beliefs and orthodox Christianity beliefs (click link to see a comparison chart). One of the most significant differences in these religions concerns the nature of God the Father. Mormons believe that He has a physical body, while orthodox Christians contend that the bible teaches that He is a non-physical being.
Heavenly father: his rule, nature, and work
"The Father has a body of flesh and bones as tangible as man's; the Son also..." --Doctrine and Covenants, 130:22
While the study of heavenly father in LDS belief can be extensive, there are three primary characteristics that are important to understand as a starting point.
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. On this issue, Mormon belief and Christian belief are very similar, if not identical. It is the next attribute where there is significant disagreement occurs.
Mormonism is unique, however, in its belief that 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.  This is why in the picture above, heavenly father and Jesus Christ are depicted as having physical bodies.
Orthodox Christian theology disagrees with this teaching, noting verses like John 4:24 - "God is a Spirit" (KJV) and Numbers 23:19 - "God is not a man" (KJV). Furthermore, orthodox Christian scholarship asserts that Mormon theology has confused the interpretation of the texts they use to support their view. They argue that passages that refer to God's "face," for example, are anthropomorphisms. An anthropomorphism is defined as "an interpretation of what is not human or personal in terms of human or personal characteristics" (Merriam-Webster Dictionary). The reason why the Bible communicates in this way is to aid the understanding of the reader.
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.
- What is God like?" Mormon.org.
- "We are created in God's image." Mormon.org.
- "God, our Heavenly Father." Mormon.org.
- Mormon Beliefs: God the Father - BBC Religion
- Nature of God - Mormon.org (click on "Index" on the left for full list of topics)
- References for Mormon and Biblical Beliefs about God - Leadership U (non-Morman website)