How do surgical scars heal?

A scar is the one result of surgery you cannot hand back, so it deserves attention at the recovery stage and before it, when the operation is still only a plan. The short answer, from MedlinePlus, is that scars usually fade over time but never go away completely.
What decides how a scar looks
MedlinePlus says how your scar looks depends on how big and deep your wound is, where it is, how long it takes to heal, your age and your inherited tendency to scar. Two of those, the size of the wound and where it sits, are worth raising with the surgeon before you commit.
What fading does and does not mean
Expect improvement, not disappearance, and judge the result over time instead of in the first days.
The change that would alter the picture
Infection at the incision is a separate question from the scar. The Centers for Disease Control and Prevention describes it in its surgical site infection basics. If the incision changes in a way the surgeon did not describe to you, call the office rather than waiting to see how it looks next week.
The question that usually follows
After scars, people tend to ask about the rest of the surgical day. MedlinePlus has an article on conscious sedation for surgical procedures, and the Cleveland Clinic offers an overview of anesthesia. Both belong to the same planning conversation as the incision.