Before elastic knitted t-shirt was invented, undershirts would have a drawstring or smocked neckline to adjust the tightness. Since you cannot wash your outer clothes as frequently you have to make sure the undershirt is protecting your clothes from stain and sweat (particularly back of the neck). In the mid to late 1500's clothes started to have a higher neckline and the undershirt neckline would have to be drawn tighter. The gathering would form a little ruffle like this that peeks out of the collar. That ruffle eventually became larger and larger before it finally became a detached item.