Joseph Smith’s explanation of the meaning for “Mormon” can be found on page 299-300 of “The Teachings of the Prophet Joseph Smith Compiled by Joseph Fielding Smith.”
**If you decide to read the above source, you will also want to read the following:
If you read all of what Joseph says on the matter, you will see that the meaning of “Mormon” is taught in conjunction with a statement on what the Bible represents. The Prophet expresses that the Bible means “good,” not linguistically, but “in its widest sense.” In light of that context, we see that the full definition of “Mormon” is not “more good” in the sense that Joseph used poor grammar, but in the sense of “additional” or “further” good/ goodness.
I hope that made sense. Basically, my first reaction was to think that he meant “more good” in the sense that he should have used “better.” But upon reviewing the full context, I realized that he was talking in relation to the Bible. “Mormon” means “more” or “additional” good (in addition to the “good” that is the Bible).
But, as Joseph declares, the root of the word “mon” means “good” the same type of “good” as we refer to when we think of the “Good Shepherd.” And it is this root that I focus on in the article.
President Hinckley also took up the subject in this 1990 conference talk, although it appears that he was unaware of what Joseph had to say on the matter.