This is the kind of insurance that compensates the injured people in your car and the other car in case of an accident. What you want to do is protect your assets from an injured party's expensive claims or lawsuit even if the accident wasn't your fault. The insurance policy will protect you for a certain amount per person in the accident as well as a cap per accident. The coverage is indicated in a "split limit". For example, your policy might say $50,000 for a driver or passenger's bodily injury and up to $100,000 for bodily injuries in total.
How much coverage should you get? It depends on your own personal assets, because that is what you are protecting. If you are at the lower end of the income scale, say $25,000 per year and don't own a home, then a 50,000/100,000 split limit might be adequate for you. However, if your income nears $100,000 and you own your home with other assets, then a 100,000/300,000 split makes more sense. If you are significantly wealthy, insurance companies offer an umbrella policy giving coverage for all kinds of liability claims for one million dollars or even more. For each succeeding million covered in the policy, the cost gets smaller.
What the insurance company charges you for this insurance can vary from state to state and even within states from rural to city. It also takes into consideration your age and driving record.