That was for the OnStar module. Since they stopped supporting it in the G8, the previous owner removed it from the car since it is unusable. There is also a battery under the rear deck cover that can be removed, but it's not worth doing until you blow a sub and have to replace it.
'09 PSM G8 GT - OPG Intake, DOD-Delete w/ Stage 1C 218/229 .600 Lift 117.5LSA, Kooks 1 7/8 Mids, Solo Axle-Back w/ X-Pipe, SuperPro Bushings (Front and Rear). BMR Sway Bars (Red)
"If you want to criticize someone else's work, be sure that your own is in order first."