So here goes. First, an introduction. Just like the first lesson I had to teach my Beehive class of girls when I was a Young Women 2nd Counselor. It was on chastity. And a few minutes into the lesson, I had to stop and ask if any of them knew what "chastity" meant. They didn't.
In my words, I define it as "no sexual relations outside the bonds of marriage," and marriage as we believe in God's law means between a man and woman.
The definition on lds.org is a bit more detailed:
Chastity is sexual purity. Those who are chaste are morally clean in their thoughts, words, and actions. Chastity means not having any sexual relations before marriage. It also means complete fidelity to husband or wife during marriage.