1. What should I call them?
The official name of the church is The Church of Jesus Christ of Latter-day Saints, which is a mouthful. "Mormon," of course, is a nickname from the church's original work of scripture. However, a lot can be gleaned from looking at the church's official title. Mormons call themselves "The Church of Jesus Christ" because they believe that Jesus did in fact organize a church while he was on the earth, an institution with a priesthood and sacraments. Mormons call themselves "Latter-day Saints" to distinguish themselves from previous iterations of that church. As he believed there was too long to wait before Jesus's second coming, "Latter-day" seemed to Joseph Smith an appropriate distinction.
The term "saint" derives from the New Testament; Paul uses it to describe any believer.
2. Who are they?
Mormonism has been, from the beginning, a not particularly American religion. In the early 1840s, 10 years after he founded his church, Smith had nearly as many followers in Britain as he did in the United States, thanks to missionaries he sent to Europe. Not much has changed. There are more Mormons outside the United States than there are inside it, about 8 million of the church's 14 million members. Spanish is close to becoming the mother tongue of a plurality of Mormons in the world. This is one reason why the church's leadership has publicly resisted the harsh immigration laws popping up in Western states with a high Mormon population. At least one lay Mormon leader has been deported from Utah, and undocumented Mormons called as missionaries have occasionally been caught in visa and immigration nets.
3. Why are they so conservative?
That said, most Mormons in the United States -- two thirds, if the recent Pew survey of Mormons can be believed -- identify with the Republican party. This has been true for a long time; it was the Republicans, after all, who shepherded Utah along the path to statehood in the late 19th century.
More recently, the Mormons have, like other conservative religious groups, found issues like abortion, the sexual revolution or the feminist movement threatening to the traditional culture to which they had given religious imprimatur, and have accordingly become social conservatives. They deeply prize the idealized vision of the nuclear family that the 1950s bequeathed us. But deeper than these issues, near their bones Mormons have an instinctive distrust of the federal government. In part, this makes them typical Westerners, inheritors of the myth of the rugged individualists who settled the plains (although they settled Utah in part with financial assistance from the federal government). But it also derives from the experience of the 1880s, when federal marshals invaded Utah with a mandate to stamp out the practice of polygamy and arrested hundreds of Mormons -- for, the Saints believed, little more than practicing their religion.
4. What do they believe?
Nonetheless, it is a mistake to assume that Mormonism is a monolithic whole. Like any faith the Mormon tradition includes within it a wide range of theological opinion.
Most Mormons tend to be theologically conservative, the result of a lack of education as much as anything else. The church runs nothing like the seminaries of other faiths, and has no trained theologians. Thus, Mormons have remained insulated from the controversies over translation, historicity and redaction that undermined confidence in biblical authority in the past 200 years. It is commonly believed within Mormonism that Moses wrote the first five books of the Old Testament, that Jesus' miracles occurred precisely as the Bible describes, and that Adam and Eve were actual people. The church officially takes no stand on the question of evolution, but most lay Latter-day Saints are sympathetic to creationism. Mormons add to these their own particular orthodoxies: the historicity of the Book of Mormon's narrative of an ancient Christian civilization in the Americas, the veracity of Joseph Smith's divine call, and other such issues. Dissent or disagreement is often met with defensiveness, or, perhaps more precisely, puzzlement. Nonetheless, the number of Mormons with academic training in religious topics is growing, and more and more Mormons seek to bring their tradition into dialogue with modern biblical scholarship, history and theology.
The Mormon tradition also contains within it a number of churches who trace their legacy to Joseph Smith. The Community of Christ, the largest of these, claims some quarter of a million members, and the best known, the Fundamentalist Church of Jesus Christ of Latter Day Saints, tens of thousands. Both diverge rather radically from the LDS Church theologically -- the Community of Christ having proclaimed itself a "peace church" deeply committed to social justice and less so to theological literalism, and the FLDS Church holding to 19th century theology and practice the LDS Church has largely left behind.
5. What does it mean to be Mormon?
The LDS Church's active membership, according to a 2008 Pew survey, is 56 percent female and 44 percent male. This is somewhat more even than many other Christian churches, which may well be due to the church's lay leadership. The Mormon priesthood is restricted to men, and more, the church's organizational structure is deeply, if unconsciously, patriarchal. Victorian-era language crediting women with superior delicacy and spirituality and consequent lack of need for real leadership roles is common. However, both men and women are given frequent and demanding opportunities to work. Men serve in general leadership positions while women run a large women's organization and children's programs. On the local level, there is no professional clergy; all the jobs, from teaching Sunday school to leading the choir to preaching on Sunday, are taken up by lay members of the congregation. Most governance is done through small committees, a system that is the inheritance of a mid-20th century churchwide reorganization called "correlation," which drew its inspiration from the corporate world.
This church culture is simultaneously demanding, exhausting and, for some, hugely rewarding. It has largely shaped Mitt Romney's character: he has worked all his life for a church with international aspirations, a deeply bureaucratic leadership marked deeply by the starchy corporate culture of the 1950s, and a wildly complicated relationship with American society. For better or for worse, this is the inheritance he would bring to the White House.