The XLR is a throttle response controller. It is installed in the footwell of your car and adapts the throttle pedal signal.
It enables the car to react much faster. It will feel more sporty and aggressive. You can compare it to the different driving modes your Stinger already has. If you think the Sport mode of your Stinger makes it already responsive enough, you do not necessarily need the XLR. However, most people just can't image how responsive their car could be. The think they don't need it, but after testing it they don't want to give it back...
It also has economy settings, which lenghten the response time. This can be used to drive conveniently in stop and go traffic. Some people (e.g. Nissan GT-R owners) are buying it for easier parking (and valet parking).