"Shiny" was a derogatory term that veteran clone troopers used to refer to their less-experienced clone rookie colleagues. It referred to the shininess of the clone trooper's armor that was not dirtied through combat, and/or the "shininess" of their experience.
When the clone troopers Hevy, Echo, Droidbait, Fives, and Cutup were given their first assignment and stationed on a remote outpost in the Rishi system, they were considered shinies. They were unaware of the meaning of the term until it was explained to them by Clone Captain Rex. However, after an attack from Confederacy forces, Droidbait, Hevy, and Cutup perished, and Echo and Fives were inducted into the famed 501st Legion, leaving their "shiny" status behind, both literally due to the state of their armor, and in terms of their battle experience.