Free electrons are those electrons in the conduction band. They’ve thrown off the shackles of their nucleus and can move wherever they want. It’s time to party!
Electron that can move freely from one atom to the next.
Grob’s Basic Electronics, 11th Edition by Mitchel E. Schultz
An electron that has acquired enough energy to break away from the valance band of the parent atom; also called a conduction electron.
Electronic Devices : Conventional Current Version, 9th Edition by Thomas L. Floyd