Bodily injury (BI) liability coverage is the portion of an auto policy that pays for injuries the policyholder causes to other people — medical costs, lost wages, pain and suffering. When you claim against "the other driver's insurance," BI coverage is what you are claiming against.
Two things follow. First, BI pays for the other side's victims, never the policyholder's own injuries — your own crash injuries from an at-fault driver come from their BI, and your own from your UM/UIM or med-pay. Second, BI is capped by policy limits, which is why the limits question dominates serious cases.
California requires BI coverage, but minimum-limit policies are everywhere. After a crash, get the other driver's insurer and policy number at the scene if at all possible — a claim can be opened with that alone.