How do GPA's work?

Depends on the scale your school uses.

Schools with a 4-point scale give 4 points for A’s, 3 for B’s, 2 for C’s, 1 for D’s and 0 for F’s. Some schools assign fractional points for pluses or minuses. Sometimes A- or B+ are 3.5 and sometimes A- is 3.7 and B+ is 3.3 depending on the school. My college didn’t consider pluses or minuses in calculating our GPAs, B- B and B+ were all worth 3 points. Your GPA is the average of the number of points for all classes attempted..

A weakness of this system is that it gives the same credit for all classes. It might be easier to get an A in basket weaving than it is for Advanced Placement Calculus. I remember my High School guidence councelor advising students to only take harder college prep classes if we were sure we could ace them since an A in the regular class will be better for our GPA than a B in the harder college prep class. Some schools use a weighted GPA where AP or honors classes get an extra point or two. In weighted GPAs an A in a harder class may be worth 5 or 6 points instead of 4. This encourages students to attempt harder classes even if they are not sure they can ace them.

Since a GPA can refer to a single semester or be cumulative sometimes CGPA is used to indicate your GPA for your entire program vs. a specific term.

This is how most US GPAs are calculated. Schools in other countries use different systems.

Generally GPAs are expressed with 3 significant digits so a single C will probably lower your cumlative GPA a few ticks and of course it would lower your short term GPA more .