Bodily injury liability is the coverage on an automobile policy that pays damages the insured becomes legally responsible for when they injure someone else in a crash. "Bodily injury" is defined by insurance regulators as "physical injury including sickness or disease to a person," and the damages it gives rise to are the injured party's, not the insured's: their medical treatment, their lost earnings, and the non-economic damages the law of the state allows for an injury, such as pain, suffering and inconvenience. It is third-party coverage, which is a distinction developed at length on the liability coverage page, and it ordinarily comes with the insurer's obligation to defend the insured as well as to pay.
It is one half of the auto liability section. The other half, property damage liability, pays for what the insured breaks rather than whom they hurt, and it is structured differently. The two are separately limited and separately required by statute, which is why they are treated as two coverages rather than one.