Brand spanking new
This is simply a more emphatic way of saying brand new where the word spanking acts as an intensifier. The first known usage of brand spanking new is 1860. Spanking in this sense has nothing to do with spanking meaning a beating or a thrashing. So the theory that spanking new derives from the practice of giving new-born babies a spank on the bottom as they are born can be dismissed as folk etymology. Spanking, according to the OED, dates from the late 17th century and is colloquial for something that is exceptionally fine in some respect. See also Spanking.