The story that I have heard - and I am not affiliated with the Citadel - is that "Big Red" as it is called appeared during the 100 year celebration of the Civil War and became the Citadel's Spirit Flag.
You may have noticed other variations of the official state flag when you have visited the state. For instance, Clemson graduates, students, or fans will have a white Palmetto and Crescent on an orange background as their front car tag or will have an Orange Palmetto and Crescent sticker on their back window.
Girls will have a Pink Palmetto and Crescent, etc.
It is a way that we South Carolinians identify ourselves to each other. No need to have a bumper sticker saying "Go Clemson" when your front car tag says it all.
I, myself, have the "basic" flag as a front car tag.