Liability insurance will pay for property damage and bodily injury suffered by others in a crash that you caused. Here are the minimum liability coverage limits the state requires: $15,000 for injury/death to one person; $30,000 for total injury/death if multiple people are hurt in the accident; and $5,000 for damage to property.
Bear in mind that 15/30/5 are the maximum payments your insurance company will make, so think about how much medical procedures cost and how far $5,000 in property damage will go. Also keep in mind that liability motorcycle insurance will not cover your own injuries or property damage. That requires comprehensive and collision coverage.
Remember California requires all operators and their passengers to wear an approved safety helmet at all times when on the road. Also, please assume that other drivers probably cannot see you, so be sure not to ride in their blind spot (the left and right rear of the vehicle).
Check with your insurance professional to see if you are carrying the required coverage for your motorcycle, and if you need to be a little more protected. Also ask if completing a motorcycle safety course will reduce your premium. Enjoy your ride!