Why did early Latter-day Saints practice polygamy?

27. Wherefore, my brethren, hear me, and hearken to the word of the Lord: For there shall not any man among you have save it be one wife; and concubines he shall have none; 28. For I, the Lord God, delight in the chastity of women. And whoredoms are an abomination before me; thus saith the Lord of Hosts. 29. Wherefore, this people shall keep my commandments, saith the Lord of Hosts, or cursed be the land for their sakes. 30. For if I will, saith the Lord of Hosts, raise up seed unto me, I will command my people; otherwise they shall hearken unto these things.

And verily I say unto you, that the conditions of this law are these: All covenants, contracts, bonds, obligations, oaths, vows, performances, connections, associations, or expectations, that are not made and entered into and sealed by the Holy Spirit of promise, of him who is anointed, both as well for time and for all eternity, and that too most holy, by revelation and commandment through the medium of mine anointed, whom I have appointed on the earth to hold this power (and I have appointed unto my servant Joseph to hold this power in the last days, and there is never but one on the earth at a time on whom this power and the keys of this priesthood are conferred), are of no efficacy, virtue, or force in and after the resurrection from the dead; for all contracts that are not made unto this end have an end when men are dead.

And again, verily I say unto you, if a man marry a wife by my word, which is my law, and by the new and everlasting covenant, and it is sealed unto them by the Holy Spirit of promise, by him who is anointed, unto whom I have appointed this power and the keys of this priesthood; and it shall be said unto them—Ye shall come forth in the first resurrection; and if it be after the first resurrection, in the next resurrection; and shall inherit thrones, kingdoms, principalities, and powers, dominions, all heights and depths—then shall it be written in the Lamb's Book of Life, that he shall commit no murder whereby to shed innocent blood, and if ye abide in my covenant, and commit no murder whereby to shed innocent blood, it shall be done unto them in all things whatsoever my servant hath put upon them, in time, and through all eternity; and shall be of full force when they are out of the world; and they shall pass by the angels, and the gods, which are set there, to their exaltation and glory in all things, as hath been sealed upon their heads, which glory shall be a fulness and a continuation of the seeds forever and ever.

The Book of Mormon makes clear that, though the Lord will command men through his prophets to live the law of plural marriage at special times for his purposes, monogamy is the general standard (Jacob 2:28-30); unauthorized polygamy was and is viewed as adultery. Another safeguard was that authorized plural marriages could be performed only through the sealing power controlled by the presiding authority of the Church (D&C 132:19). Once the Saints left Nauvoo, plural marriage was openly practiced. In winter quarters, for example, discussion of the principle was an "open secret" and plural families were acknowledged. As early as 1847, visitors to Utah commented on the practice. Still, few new plural marriages were authorized in Utah before the completion of the Endowment house in Salt Lake City in 1855. With the Saints firmly established in the Great Basin, Brigham Young announced the practice publicly and published the revelation on eternal marriage. Under his direction, on Sunday, August 29, 1852, Elder Orson Pratt publicly discussed and defended the practice of plural marriage in the Church. After examining the biblical precedents (Abraham, Jacob, David, and others), Elder Pratt argued that the Church, as heir of the keys required anciently for plural marriages to be sanctioned by God, was required to perform such marriages as part of the restoration. He offered reasons for the practice and discussed several possible benefits (see JD 1:53-66), a precedent followed later by others. But such discussions were after the fact and not the justification. Latter-day Saints practiced plural marriage because they believed God commanded them to do so. Generally plural marriage involved only two wives and seldom more than three; larger families like those of Brigham Young or Heber C. Kimball were exceptions. Sometimes the wives simply shared homes, each with her own bedroom, or lived in a "duplex" arrangement, each with a mirror-image half of the house. In other cases, husbands established separate homes for their wives, sometimes in separate towns. Although circumstances and the mechanics of family life varied, in general the living style was simply an adaptation of the nineteenth century American family. Polygamous marriages were similar to national norms in fertility and divorce rates as well. Wives of one husband often developed strong bonds of sisterly love; however, strong antipathies could also arise between wives.

Question: Was the reason Mormons practiced polygamy to look after widows and orphans, make sure more children were born and because there were "extra women" in Utah?

From the early 1840s to about 1890, in response to revelation given to the Prophet Joseph Smith, leaders of The Church of Jesus Christ of Latter-day Saints taught the practice of plural marriage, also called polygamy. Over a period of about 50 years, 20 to 30 percent of Latter-day Saint men, women, and children lived in families that practiced plural marriage.