The offensive backfield in football is the area of the field behind the line of scrimmage on the side where the offense is. Any player not on the line of scrimmage is considered to be in the offensive backfield. Those players are generally the "backs" like the quarterback, running back, and the fullback.
The quarterback is the only offensive player in the backfield, the running backs are either lined up elsewhere or replaced for another position.
Instead of a normal shotgun, which is about seven yards, the quarterback is lined up four yards behind the line of scrimmage. Behind the quarterback is the running back, who is lined up another three yards behind.
All three members are in the back field, the quarterback is in the shotgun with the fullback on one side and the running back on the other.