Traditionally, a witcher uses two swords, a silver sword for use on some kinds of monsters and other supernatural foes, like necrophages, therianthropes and cursed ones, shapeshifters, wraiths or vampires. The steel sword is used for creatures not sensitive to silver or shelled so heavily that only the hard steel can harm them.
The "silver" swords which witchers make for themselves (or contract swordsmiths to make for them) are traditionally made from meteoric iron, which is then coated in silver and inscribed with magical runes. A purely silver sword would be entirely too soft and therefore useless. It is still very delicate however so witchers have to use them carefully - for example, crossing other sword would easily damage it.
Within the games, there are a number of silver swords that Geralt can use. Unlike in the novels, they are used against all of monsters and contact with other sword doesn't really harm the blade.