Collar stays are smooth, rigid strips of metal (such as brass, stainless steel, or sterling silver), horn, baleen, mother of pearl, or plastic, rounded at one end and pointed at the other, inserted into specially made pockets on the underside of a shirtcollar to stabilize the collar’s points. The stays ensure that the collar lies flat against the collarbone, looking crisp and remaining in the correct place. Often shirts come with plastic stays which may eventually need to be replaced if they bend; metal replacements do not have this problem.[1]
Collar stays are removed from shirts before dry cleaning or pressing, as they could damage the shirt in the process, and then replaced prior to wearing. Shirts that are press ironed with the collar stays are vulnerable to damage, as this results in a telltale impression of the collar stay in the fabric of the collar. Some shirts have stays which are sewn into the collar and are not removable. (source: http://en.wikipedia.org/wiki/Collar_stays )
How to use a collar stay:
Simply slide in the collar stay in the pocket on the underside of the dress shirt collar. After that, fold down the collar as normal. Remember that pointed shirt collars require pointed shirt stays. Rounded shirt collars call for rounded collar stays.