The meaning of extensive is large or wide or covering a very large area.
Or another way to say fairly extensive would be that the car someone was driving when it got into an auto accident suffered fairly extensive damage.
That means that the damage was extensive but just fairly extensive which means the car didn't suffer too much damage although it suffered a great deal of damage.
If the car suffered extensive damage then the car would be damaged more.
The word fairly usually means moderate so the car would suffer moderate damage over a large area of the car.