Given to Geralt at the beginning of Chapter II to fight The Beast of the Sewers. A silver sword is one of the two main tools of the witcher. It is a delicate blade only used against creatures who are vulnerable to silver, such as the undead and most types of monsters. It is light enough to be wielded in only one hand, leaving the other hand free for another weapon or for the casting of Signs.
The witcher's silver blade actually has a steel core which is plated with a thick layer of silver which is lethal to magical beasts. This weapon was made specifically for slaying monsters born of magic, those which can not be hurt with common steel weapons.
In the second game its called Witchers' silver sword. If you start the game without importing a save file from the original game, Geralt must gather the components to craft such a sword to complete the quest A Sword for Monsters in Chapter I. The list of components is found in the document Diagram: Witcher's silver sword.