This post is intended as an introduction to people who really don't know what is meant by the term Mormon, and for those who have heard the term, and may have even known a Mormon, but still have little or no idea of what a Mormon is.
First of all, the term Mormon is most often applied to people who are members of The Church of Jesus Christ of Latter-day Saints. As the name of the church implies, we follow the teachings of Jesus Christ, and recognize Him as our Lord and Savior and we accept the writings in the Bible as scripture. In addition to the Bible we use the Book of Mormon as another book of scripture to confirm or demonstrate our faith in Jesus Christ. It is because of this book we have the nickname "Mormon", which is perfectly acceptable to us, though formally the members of the church are known as Latter-day Saints, or LDS for short.
The Church of Jesus Christ of Latter-day Saints was founded in 1830 by Joseph Smith, who we consider to be a prophet, much like the prophets in the Bible. While The Church of Jesus Christ of Latter-day Saints was officially founded in 1830, we claim that the church is a re-establishment of the original church founded by Jesus Christ almost 2000 year ago. We do not claim to be a break-away sect of any church, or a Protestant denomination, but literally the re-establishment of the ancient church. Thus we believe that we teach those things that were originally taught in the ancient Church of Jesus Christ.
As a members of the church, Mormons meet in their respective congregations every week where everything is done by the local church members. In the church we have what is called a lay ministry, meaning there is no professional, paid clergy. All talks, sermons, lessons and organization is done by members who volunteer their time and effort. The local congregations are lead by someone who we refer to as a bishop, and like all other leaders in the church they are not compensated monetarily for their work. The local bishops have normal jobs just like everyone else. My current bishop works for Microsoft, and I have had other bishops that were plumbers, college professors, architects, anesthesiologists and a used car salesman.
Perhaps some of the things that we are most well known for is the fact that we do not drink alcohol, tea or coffee. We also do not smoke or use tobacco. This general code of health is referred to by Mormons as "The Word of Wisdom", which includes general advice on living a healthy lifestyle. As a side note, while coffee and tea are expressly forbidden by the Word of Wisdom, most members have extended this to include all caffeinated beverages though this is not required by the church. Still, most Mormons refrain from drinking anything caffeinated, though it is not unusual to meet some Mormons who do. Mormons do not have any prohibitions against eating meat of any kind, and other than having the general rule to live and eat healthy, it is largely up to the individual members to decide for themselves what that means.
As for holidays, Mormons celebrate them. We do not have any prohibitions against celebrating any holidays. We celebrate Christmas as the anniversary of Christ's birth and Easter as the anniversary of his resurrection. All other holidays Mormons celebrate depend on the country in which they live. For example in the United States Mormons celebrate the Fourth of July while in Argentina they celebrate the 25 of May (and July 9th and October 26th, I mean who has three independence days??? That is, other than Mexico and France.). In the US we even celebrate Halloween by going trick-or-treating (I mention this because someone once asked me about this). With all of these holidays while the individual members celebrate them, there is no official church doctrine mandating the celebration of particular holidays (i.e. unlike for example, the Catholic Church, or Eastern Orthodox Church which observe holy-days, or saints' days as a matter of religious observance). In short, we celebrate holidays like most other people around us.
As individuals, Mormons get involved in politics like anybody else, but as a church, The Church of Jesus Christ of Latter-day Saints makes it a very strong policy to not get involved in political matters, and will only speak out on topics that we consider to be of extreme moral importance, or in matters that will damage our freedom to worship. Other than that the church does not endorse any politician, political party or platform. While individual Mormons tend to be conservative politically, this is not a rule. Some famous Mormons include well known conservatives like Orrin Hatch (R-Utah) and well known liberals like Harry Reid (D-Nevada) (Currently Harry Reid is the Senate Majority Leader).
One of the things Mormons focus on a lot is family. We place great importance in taking care of and teaching our families. For us there is nothing more important than taking care of our families. We encourage fathers to love and respect their wives and their children, and we teach wives to love and respect their husbands and their children, and we teach children to love and respect their parents. We believe that families and family ties will survive beyond death, which means that when Mormons are married they are not married "'Till death do you part." as is common in other churches, but for "Time and all eternity". It is because of this we place so much importance on our families.
And this brings us to the last thing I wanted to mention and that is Mormon church buildings. Our standard church buildings are called chapels, and this is where we meet every week for our church meetings. We also have church socials there and other activities, such as Boy Scouts and Cub Scouts. The local Cub Scout district holds the annual pinewood derby in the chapel that I go to. Thus the local church buildings are general, all-purpose buildings for anything church related. In addition to our local church buildings we have buildings known as Temples. These are different from our local church buildings in that only members of the church who actively try to live the principles of taught by the church are allowed to enter. There are no typical church meetings that happen in Mormon temples, but they are intended to be places of where we learn and pray and commit ourselves to God. Temples are also where Mormons go to be married. This shows the importance we place on marriage in that we only perform it in our temples, which we consider to be among our most sacred spaces. While there are literally thousands of our local chapels in the world, there are only about 130 temples in the world. The closest one to where I live in located in Raleigh (actually Apex), North Carolina.
I hope that this post has be helpful in answering some of the most basic questions about who Mormons are. I have most definitely not covered everything about Mormons, but if you have any questions feel free to contact me or to leave a comment.