The rental counter asks whether you want their cover and charges a daily rate for it. Whether you need it depends on what your own policy already does, and most people answer without knowing.
Your own liability and physical damage cover usually extends to a rental car in the United States. Usually is not always.
Three things about driving a car you do not own.
Liability extends to a rental car you are driving, and if you carry collision and comprehensive on your own vehicle, that normally extends too, subject to your deductible. A household with no physical damage cover on an old car has nothing to extend, which is exactly the household most likely to decline the counter offer.
Rental companies bill for the income lost while a damaged car is repaired. Some personal policies pay it and some do not, and credit card cover frequently does. It is the most common unpleasant surprise in a rental claim.
A United States auto policy generally does not follow you to another country. Rental cover bought locally, or a card benefit that explicitly covers the destination, is what answers there. Mexico in particular requires an admitted Mexican policy.
What you already have before you buy it twice.
If not, there is nothing to extend to a rental.
It varies, and it is the charge that catches people.
Outside the country the answer changes completely.
Tell us whether you carry collision and comprehensive, and where you travel.
