This Stainless Steel "White Wolf" necklace is a witcher medallion given by the school of the wolf in Kaer Morhen where he was trained.
Geralt's origins in The Witcher are as tragic as one might expect from a child being subjected to mutations that could kill them. Geralt was born to the sorceress Visenna and, though his father is unspecified, it is likely that he was the warrior Korin, two powerful figures in their own right. Geralt was left at Kaer Morhen, the Witcher training school, by his mother after being born. There, he went through training and was made into a witcher through the Trial of Grasses, where young boys are subject to mutations that will make them stronger and faster in order to better combat monsters. Only three out of ten boys survive the process, but Geralt is notable for having a remarkable tolerance to the process, which caused him to be further experimented upon and given even more mutations. This is what turned his hair white.