When you have a choice of thresholds, you are deciding which is more important: your right to sue for pain and suffering, or paying less money for your car insurance coverage and having fewer rights to pursue damages if you are hurt in an accident.
That's because, in an effort to reduce the cost of car insurance, some states have placed restrictions on people's ability to sue for non-economic losses, such as pain and suffering. The threshold level basically represents the degree of bodily injury you must establish before being allowed to sue the negligent party and recover non-economic damages.
Having no threshold typically means that in your state you have the option with your car insurance policy to choose to not have to meet a predetermined level of injury in order to claim or sue. This type of choice is usually made if you live in a no-fault state, not in a tort state.
State laws vary, so in your state the threshold may be verbal (regarding the severity of the injuries) or a dollar amount (i.e. $10,000), or both. For example, with a monetary threshold of $5,000, an injured person may sue if his/her injuries and other economic damages (rehabilitation expenses, loss of income, etc.) exceed $5,000.
Some no-fault states have made their threshold a mandatory requirement that everyone must meet to recover damages while other states have adopted a dual threshold requirement, allowing you to choose between two or more options that control your individual right to recover damages.
You appear to have an option, so perhaps you are from the state of New Jersey. When buying insurance here, there are two choices: the Zero threshold option (no limitation on lawsuit); or Lawsuit threshold (limitation on lawsuit).
Selecting the no (zero) threshold option in auto insurance allows you, if injured, to retain the right to sue the at-fault driver to try to recover damages (pain and suffering) no matter what type of injury was suffered. To get monies you will have to successfully prove your case in court. With no-threshold coverage you maintain your right to sue, but a downside is you will pay increased car insurance rates.
The lawsuit threshold in New Jersey limits the right to recover damages for pain and suffering to very specific types of injuries that state legislature has decided are permanent or serious injuries. For giving up some of your rights, you will pay less for your car insurance coverages.
This information is specific to New Jersey since it is the state normally thought of when one mentions zero or no threshold. If you live in a different state and want to know more about your state's threshold levels, speak with your agent or contact your state's insurance regulatory body.