In New York, it means the trial is split in two parts.
The first part is liability. That will determine who, if anyone, is responsible for causing your accident.
Assuming the person you sued has been found at fault, then the trial moves to the second phase; damages.
The second part is designed to determine how much compensation you are to be awarded.
The same jury will often be used to try both parts of your car accident case.
Sometimes however, the trial will need to be conducted at different times. In that instance, there will likely be two different juries.