What Does Shaving Down the Sides of the Nose Mean?

Talk to your surgeon as he may be talking about changing the outside of your nose to improve the cosmetic appearance.  There is nothing wrong with that as long as that is what you want.

Miscommunication is a common problem. It is imperative that you tell your doctor to explain to you in laymen terms exactly what she or he plans to do.
With you describing 'shaving the sides of the nose' is not clear. It can be nasal bones, upper lateral cartilages, alar wedge resections or low lateral osteotomies.
So, please ask your doctor for details.
Regards

"shave down the sides of my upper nose cartilage" can mean many things. Don't assume anything. Ask your nasal surgeon the details of the proposed procedure. Does the planned surgery meet your goals and expectations? Best of luck.

"Shaving down the sides of the nose" is not a clear statement. Doing a septoplasty and turbinate reduction is for improving the nasal airway and is not a cosmetic operation. Doing procedures to change the external appearance of the nose (Rhinoplasty) is a different operation that may or may not be done at the same time as the septoplasty. It needs to be clear if you are asking for cosmetic surgery, and if so, what you want changed such as thinning or reducing the dorsum, refining the tip, making the nose smaller, etc.
Make sure you are clear on the plan before agreeing to surgery.