"How will 2 points on your driving record in the last 2 years affect your license and insurance in California?"
Your insurance premium is based on a number of factors only one of which is your driving record. If you have points on your license then your insurance will be higher than someone with other identical factors but no points.
But if the 2 points where added because of 1 violation (reckless driving, over 100mph, ect but not including DUI) they will stay on your record for 7 years not 2 like 1 point violations and will make your insurance even more than 2 points overall on your record, from different violations added up(speeding 1pt, stop sign 1pt, Red light 1pt, ect)
My insurance carrier (21st) in Calif increased my rate ~40% due to a single point (redlight camera ticket)