Traditionally, a witcher uses two swords, a steel sword for use on monsters sensitive to iron, and a silver sword, which is suitable for most monsters not sensitive to iron.
The steel swords which witchers make for themselves (or contract swordsmiths to make for them) are traditionally made only from meteoric iron, which grants the weapon superior, even magical qualities. It may also be possible that iron-fearing monsters are affected more strongly by meteoric rather than earthly iron.
In the novels it is mentioned by Geralt that the steel sword is often mistaken for being primarily intended for fighting hostile people. It is true that witchers use their steel swords when fighting against armed opponents, but this is only because a silver sword is a relatively delicate instrument. Striking metal armor or parrying an opponent's weapon will quickly ruin a silver sword, unlike a steel sword which can withstand such use with little to no damage.
Within the games, there are a number of steel swords that Geralt can use: