Shyness was a feeling of fear or discomfort when being around other people, especially in new situations or among strangers.
According to an account that was anything but canon, while Montgomery Scott was playing the drums on the bridge with a Post Mainframe Acid-Cardassian Ten Forwardcore band, D'Vana Tendi showed shyness at the moment and told him "you're really hot." This was surprising to Hikaru Sulu, who then said "Oh my." (VST: "Walk, Don't Run")