Maxwell is a character in the game Don't Starve. He is the demon who transfers all of the other characters to the world of Don't Starve. It is highly likely that he was previously known as the Magician William Carter before his arrival in the world of Don't Starve. He is likely responsible for most of the harmful or dangerous creatures in the world and even possibly for the worlds themselves.
Through completing Adventure mode, you can discover his motives for what he does and acquire him as a main character. When playing as the character, he is unsurprisingly called Maxwell but in the game code, the playable variant is called "Waxwell". This is both likely to differentiate between the two for coding purposes but also so that he fits in with all of the other playable characters whose names all start with the letter "W".
