Why does the doctor check your mouth before you go to surgery?

I have a question, why does the doctor check your mouth before you go to surgery? Before my girlfriend had her surgery the doctor came in and had her tilt her head back and open her mouth as wide as possible

Maybe it's because they put a tube down your throat to help you breath when they give anesthesia. They want to check the state of your airways probably.

Operations with general anesthesia make that once asleep with intravenous sting or infusion the ansyhesist doctor intube you to continue the work through the lungs. Before that they make sure that they will not damage a dental prosthesis or interfere with it.

Exactly. They use a metal laryngoscope to visualize the airway and vocal cords, between which the airway tube must go. It's not always easy, especially in patients who have a lot of tissue in the back of the throat. The anesthesiologist needs to assess that as well as documenting the dentition and removing bridges, dentures etc. It's certainly possible to break dentures or even teeth with a laryngoscope. The anesthesiologist needs to assess the situation.

It's a Mallampati scoring system used to assess for difficult airway during intubation. There are a few other scoring systems that factor in as well to determine risk of intubation and best method for doing so. The classic Mallampati criteria assesses the airway patency based on visibility of the soft palate, uvula, and tonsils with the tongue either in a maximally protruded position or in a neutral position depending on if you use a classic or modified version of the scoring system. Inability to visualize these structures suggests a large tongue or crowded airway that could cause obstruction.

So what do they differently if they suspect an obstruction in the airway path?

They might decide to use different size equipment or they can intubate through the nose. If it's bad enough they can decide surgery is too risky and call it off.