In general auto insurance premiums do tend to be lowered once a driver has turned the age of 25. Statistically speaking young drivers, those under 25 years of age, are more prone to accidents due to immaturity and inexperience at driving. Risk assessors have determined that those 25 or older tend to be more responsible and thus their risk of at-fault accidents decreases.
Typically there is not per say a discount given when a person reaches the age of 25 but the driver's rates may be calculated in a different driver class. Insurance companies commonly at least partly base their premium rates on driver classes.
Marital status, age, sex and accident statistics help classify drivers. Insurance companies rating systems and factors can differ (as well as the state laws regulating them) so you would need to check with your current insurance provider to see if your rates will go down once you turn twenty-five.
We have seen rates lowered as much as 20% once the driver on the policy reaches the age of 25 but this is if the person has a clean driving record. If the individual's driving record shows accidents and various traffic violations than the rates may not be lowered due to the bad driving record canceling out any lowered rates coming from the increase in age of the driver.
If you have just turned 25 you can inform your insurer but normally premiums are not adjusted mid-term so you would have to wait until the policy renewed or your started a new policy to see a change in the rates. If you live outside of the US, then the age at which rates are lowered may be older, such as 30 years of age, so check with your insurer to find out about their rating system and driver classifications.