Witcher trophies are very precious rewards obtained by killing strong monsters during witcher contracts. Each trophy gives a passive bonus to character statistics, but Geralt can have only one such item placed in the active inventory slot. It means that other trophies become unneeded and some of them (at least the ones you are sure you won't be using) should be sold, especially since they waste some place in the inventory.
Trophies can theoretically be sold to most of merchants but most of them offers very low price for the items. The only person that will pay some good money for trophies is Alchemist found near the Free City of Novigrad. Look for him in the small building east from the city and north from Oxenfurt Gate. If you won't find him there, use meditation to wait 8 or 12 hours and try again.
Important - it is easy to reach the coin limit of alchemist by selling him more than one trophy at once. Because of that, you should return to him after each completed witcher contract. You can use meditation as well to wait few days for his wallet to replenish or you can buy some alchemy ingredients from him.
Important - the full list of witcher trophies (including the places where you obtain them and the bonuses they give you) can be found in the guide with walkthrough and world atlas.