Witcher 1 - You play Geralt of Rivia...a Witcher known as The White Wolf. A Witcher is a demon or monster hunter killer. You were specially trained and potions mutated you to be faster and stronger than normal humans. Geralt is the best of them. But one day while defending a town and your love you died....then disappeared. Now you are found alive but with no memory of what happened.
Witcher 2 - You saved a King and now work for him until fortunes change. You remember bits and pieces of your life as the game goes. You remember The Hunt. Some kinda badass warriors come to this world from time to time and destroy whole towns, kill many and take others with them for sport. they are either from another world or another dimension/realm. Sorta like a Predator. No one ever returns....except you did in the first game. You have offered up yourself for The Hunt if they left your love alone. But you finally escaped and came home.
Witcher 3 - Now you search for your true love while The Hunt searches for you and destroys all in it's path as they do so. Well thats all Ive gleaned...not read any real info yet...Lots of videos though

Killing Monsters trailer
The Hunt trailer
Dev info video