A frog is a simple device used as a backing for various pins, commonly refered to as "one of those thingies that go on the back of the pin." The principal purpose of a frog, thus, is twofold- to hold the emblem onto one's clothing, and also to prevent said individual from being impaled
by a mere docorative item.
Frogs commonly come in four varieties, the names of which I don't know. Less common... and for good reason... is the silicon rubber frog. The simplest type, it is merely a piece of silicon rubber shaped like a frog. (Actually the shape is basically a small disk about 3/8 inch in diameter with some manner of semicircular protrusion from the non-flat side, which serves as a grip.) The silicon frog works by mere friction, and will not hold a button of much mass or against much force, and appears on the cheapest of pins.
More common, practical, and expensive is the metal frog, which can be open or closed on the back. An "open" frog allows the point of the pin to pass through. This makes it easiest to align it, and provides for a very secure grip; however, it leaves a possibility of some degree of personal injury from impalement or scratching, but allows the pin to remain sharper, helful for use on thick clothing.
Metal frogs are most common in the "closed" variety, in which the pin does not pass through the rear of the frog. This is clearly the safest type of frog, but is more likely to fall off than an open frog and may eventually dull your pins. Most metal frogs use a simple clamping mechanism consisting of two bits of spring metal, which press against the pin, extending beyond it so that it can be squeezed to release much like some types of hose clamp. These frogs are probably the most common, and can be purchased at most uniform stores for about $0.05 each.
Premium metal frogs, commonly found on expensive jewelry bits, may use a screw or spring mechanism to adhere. These frogs are heavier and have a machined appearance, matched by greater cost- but pose the least risk of either impalement or detachment.
Sadly, most quality frogs will only work properly with certain types of pin; as such, I cannot purchase premium frogs for my ribbon bar or nametag.