Firstly, welcome to the forum and to A4 ownership. We encourage new owners to post up pictures of their cars so feel free to do so in the appropriate thread.
It's correct name is pre-sense and I have direct experience on the efficiency of the system. It will do the following under certain conditions,
"The front seat belts are electrically tightened, and the windows and sunroof are closed. The hazard lights are also activated.
If a collision cannot be prevented and an accident is inevitable, the multicollision brake assist system supports the driver with controlled application of the brakes. This can help to prevent the car from skidding, which prevents further collisions."
As Wes states, it pays to read the manual as you are driving a technologically advanced car and it save you from asking questions that are answered either in the manual, or in here in a previous thread.