Some take it as the height of effrontery that The Church of Jesus Christ of Latter-day Saints refers to its members as "saints." By what justification can Mormons dare to compare themselves to the people traditionally referred to as saints, people who are no longer alive? What makes us think that we can describe ourselves as holy? And what does that suggest about how we think about those who are not Mormons? Do we think that we are the only holy people, with everyone else profane?
Frankly, I don't think most Mormons think much about the meaning of the word saints, though it isn't uncommon for us to use the title to refer to the members of the Church, and we also recognize that the saints of traditional Christianity are another kettle of fish entirely. We rarely, if ever, use the word in the singular, and we never use it as a title. No one is going to refer to Sister Smith as "Saint Smith." And we certainly don't think that being "one of the saints" means that we are necessarily any holier than those who are not one of us.
If asked why we refer to the members of the LDS Church as saints, most of us will probably respond "Because that is what they were called in the first century church," as in Acts 9:32. That's enough reason for most of us: we believe we are a restoration of the Primitive Church; the Primitive Church referred to its members as saints; so we use the same term. But, of course, that answer begs the question. It doesn't tell us why the Primitive Church used the word to describe its members.
There is good reason to believe that to be a saint is to be a holy person. That is at least one meaning of the term. The Greek word translated saint (hagios) means "one devoted to the gods" and indicates purity of character.
Similarly, in the Hebrew Bible, the word for "holy" (qodesh) is used mostly to refer to God, but it can also be used in other ways. Besides God, the Hebrew Bible refers to both people and things as holy (for example, Exodus 3:5, 19:14 [translated "sanctified" in the KJV], and 26:33; Leviticus 19:2; Deuteronomy 33:2-3; and Isaiah 48:2, 62:12, and 64:10). But that meaning isn't enough to explain why God's people are called saints.
In the Hebrew Bible, when used to refer to people or things, the word holy means something like "set apart for holy purposes," always to God and often for purposes of temple ritual. Because holy objects have been set apart, they can be used properly only in certain ways. But it is important to recognize that holiness derives from being set apart, not from the character of the object in question.
For example, the altar is holy because it has been set apart for use in the temple, not because it has a certain shape or is made of a particular material. Any use of the altar not in line with its prescribed use as a holy object is forbidden. Similarly Israel is holy because it is chosen, not the reverse. Being called and set apart for particular divine purposes makes Israel holy, and that holiness puts them under solemn and divine obligation, the obligation to live up to the holiness to which they have been set apart. If Israel obeys God, that obedience is the proper response to their calling—to the fact that they are holy—but that obedience is not what makes them holy.
Similarly, a reasonable translation of the Greek word hagios in the New Testament might be not just "holy," but more informatively "one of God's people." As such, the saint is holy—in other words, set apart, even if not perfectly pure—and, therefore, he or she is obligated to God to be pure.
Surely the purity of character identified with saintliness is at least part of what the word saint intends. Members of the LDS Church have been called to be pure. That is expected of them. But, given the connotations of the word saint in the Hebrew Bible, we must remember that saint describes not just moral cleanliness (in the broadest sense), but also and especially a covenant relation to God. The chosen people—called saints in the Hebrew Bible, the New Testament, and today—are those who make covenant with God.