What is a Mormon? The word "Mormon" itself is likely a name invented by one of the supposed authors of "The Book of Mormon", the founding scripture of The Church of Jesus Christ of Latter Day Saints, or more commonly referred to as the LDS Church, or Mormon Church, headquartered in Salt Lake City, Utah. The name "Mormon" is given to one of the closing characters in the Book of Mormon, the described author and compiler of the records that it is supposedly ascribed from, hence the name, "Book of Mormon". Modern authorship of the Book of Mormon is most often attributed to Joseph Smith Jr, born in 1805 and raised primarily in Palmyra, New York, who claimed to have received "Golden Plates" from an angel from which he translated the book. However, word pattern analysis of the Book of Mormon reveals other more likely authors among the men closest to Joseph Smith: Sidney Rigdon, Oliver Cowdery, and Parley P. Pratt. Solomon Spalding is also theorized in the word pattern analysis as being the original author of the Book of Mormon, but under the title "View of the Hebrews", but was never able to publish said manuscript before his death.
A "Mormon" then, in modern terms, is anyone who professes faith or belief in The Book of Mormon being revealed and God sourced scripture. Mormons are not solely members of The Church of Jesus Christ of Latter Day Saints, though they would surely like it to be, as their attempt to trademark the term suggests. Fundamentalist Mormons, those who still follow the tradition of polygamy as started by Joseph Smith, also refer to themselves as "Mormon". For this reason, "Mormons" are often immediately affiliated with polygamy, though that practice was abandoned at the turn of the previous century among members of the official LDS Church.
Feel free to join and ask any questions you may have about Mormons. Most here on LifeAfterMormonism.net have spent a good portion of their life growing up and living Mormonism to the fullest, and they are very adept at sharing their experience, sans faith promoting filters. You can also start at this link when asking "What is a Mormon?".