Wikipedia definition [as of May 10, 2013]: In Mormonism, Heavenly Mother or the Mother in Heaven is the mother of human spirits and the wife of God the Father. Those who accept the Mother in Heaven doctrine trace its origins to Joseph Smith, the founder of the Latter Day Saint movement. The doctrine was not widely known, however, until after the movement's succession crisis upon Smith's death in 1844.
In The Church of Jesus Christ of Latter-day Saints, she is sung about in one church hymn and briefly discussed in church teaching manuals and sermons.
UPDATE: An essay was written and published on the LDS Church website on Mother in Heaven on October 23, 2015. Please read MormonThink's response to this essay:
Reference found in The Latter-day Saint Woman, Basic Manual for Women, Part A
President Spencer W. Kimball, speaking to Latter-day Saint girls in Mexico City, said: “You are daughters of God. … You are made in the image of our heavenly mother. … Your body is sacred to you and precious” (in Conference Report, Mexico City and Central America Area Conference 1973, 108). Reference: LDS.org
That Heavenly Mother exists is current doctrine. References to Her can be found in current manuals within the teaching programs of the Church. It is okay to talk about Her. However, current doctrine is that prayers should not be offered to Her, as that is against the pattern for prayer set by Christ. Here is Gordon B. Hinckley from 1991 and, as far as I know, is the current position of the Church on this subject:
However, recently I heard that someone had secured a copy of my talk, looking upon that as a singular accomplishment, as if it had been given in a secret and sinister manner, designed to keep it from the world. This is nonsense.
I am therefore on this occasion going to take the liberty of rereading that portion of the talk which pertains to a matter over which some few women of the Church appear to be greatly exercised. I give it to all, in this forum, because of the activities of a few who evidently are seeking to lead others in the paths which they are following. I speak of those who advocate the offering of prayers to our Mother in Heaven. I quote from that earlier address:
“This [practice] began in private prayer and is beginning to spread to prayers offered in some of our meetings.
“It was Eliza R. Snow who wrote the words: ‘Truth is reason; truth eternal / Tells me I've a mother there.' (Hymns, 1985, no. 292.)
“It has been said that the Prophet Joseph Smith made no correction to what Sister Snow had written. Therefore, we have a Mother in Heaven. Therefore, [some assume] that we may appropriately pray to her.
“Logic and reason would certainly suggest that if we have a Father in Heaven, we have a Mother in Heaven. That doctrine rests well with me.
“However, in light of the instruction we have received from the Lord Himself, I regard it as inappropriate for anyone in the Church to pray to our Mother in Heaven.
Reference: 'Daughters of God', October 1991 Ensign
The LDS hymn #292 'O My Father' is probably the place most LDS are familiar with hearing about Heavenly Mother as she is rarely talked about at church. Here are the lyrics:
O my Father, thou that dwellest
In the high and glorious place,
When shall I regain thy presence
And again behold thy face?
In thy holy habitation,
Did my spirit once reside?
In my first primeval childhood
Was I nurtured near thy side?
For a wise and glorious purpose
Thou hast placed me here on earth
And withheld the recollection
Of my former friends and birth;
Yet ofttimes a secret something
Whispered, "You're a stranger here,"
And I felt that I had wandered
From a more exalted sphere.
I had learned to call thee Father,
Thru thy Spirit from on high,
But, until the key of knowledge
Was restored, I knew not why.
In the heav'ns are parents single?
No, the thought makes reason stare!
Truth is reason; truth eternal
Tells me I've a mother there.
When I leave this frail existence,
When I lay this mortal by,
Father, Mother, may I meet you
In your royal courts on high?
Then, at length, when I've completed
All you sent me forth to do,
With your mutual approbation
Let me come and dwell with you.
Text: Eliza R. Snow, 1804-1887
Music: James McGranahan, 1840-1907
Some who have speculated and openly discussed Heavenly Mother have been disciplined severely by the Church. An excerpt from the article:
In the late 1980s, some Mormon women began exploring the history and theology of Heavenly Mother. A few even mentioned her in prayers and speeches, which triggered consternation among male LDS leaders.
In 1991, then-apostle Gordon B. Hinckley, who would rise to church president four years later, affirmed the church's teaching about Mother God, saying, "Logic and reason would certainly suggest that if we have a Father in Heaven, we have a Mother in Heaven. That doctrine rests well with me."
But Mormons do not pray to her, he said, "because Jesus Christ…taught us to pray to our Heavenly Father."
A few months before Hinckley's speech, Janice Allred, a devout Mormon living in Provo with her husband and nine kids, gave a Mother's Day talk in which she discussed Heavenly Mother. It was well-received, she recounts in a recent Sunstone article titled "The One Who Never Left Us." Several congregants even asked for copies.
A year after Hinckley's remarks, however, Allred gave a speech at Sunstone Symposium, "Toward a Mormon Theology of God the Mother."
In it and subsequent pieces, Allred didn't advocate praying to Mother in Heaven, nor say she did so herself. She did, however, argue that God the Mother is the Holy Spirit.
"I proposed that the Eternal God is both a Man and a Woman — the Eternal Father and the Eternal Mother. They are both fully God and they work together to bring to pass our immortality and eternal life," Allred said of her 1992 speech. "To do this, the Father sacrifices his eternal body to become the Son to redeem us from our sins, and the Mother sacrifices her eternal body to become the Holy Spirit to comfort, enlighten and sanctify us."
Allred's was excommunicated in 1995 for such writings.
A few years later, Allred's sister and respected Mormon feminist Margaret Toscano, was also excommunicated in part for writings about God the Mother. Others were reprimanded or threatened with discipline, and much of the public discussion went underground or went away.
Editor comment: The concept of a Heavenly Mother can be a bit strange for some people to accept, but the idea of Heavenly Mothers (plural) is very unnerving. Logically, if God has multiple wives (as taught by many early LDS leaders) then although everyone has the same Father-in-Heaven, most people would have different 'Mothers-in-Heaven'. Perhaps that's one reason we're told not to pray to our Mother-in-Heaven as we wouldn't know which one.
For more information on the origins of Heavenly Mother see MormonThink's Response to Essay on Mother in Heaven