States typically have either a comparative or contributory negligence laws. Comparative negligence laws mean that parties involved in an accident may share the cost of damages from an accident in proportion to the share of their negligence. A motorist determined to be 50% or less at fault may recover their damages minus the percent cause by their own negligence. If more than 50% there would be no recovery for losses from the other party usually.
Contributory negligence is much stricter and means that if you are even slightly at fault in a collision you are not entitled to any recovery against the other driver even if they were mostly at fault for the incident.
Ultimately for claim purposes the insurance companies involved will investigate the accident claim to determine fault. This is done by the insurance adjusters whose job it is to determine the extent to which you are covered and the degree of fault of each driver. Sometimes an adjuster will split up fault differently than the police or determine fault to be placed on a different person then what the police report states.
An adjuster's investigation and determination of the claim usually takes into account both drivers' recollection of the accident, any witness statements and the damage of both vehicles. Insurance adjusters will also be guided by state laws. Since you were found 10% at fault in a comparative negligence state you should ask the claims adjuster what parameters were used to determine each party’s degree of responsibility.
Comparative negligence (also called comparative fault in some areas) usually comes into play when it is contended by a driver or the insurance company involved that two or more parties failed to perform at the standard of the "ordinary reasonable person". Since the insurance company is bringing up "last clear chance" this may mean that they believe from their finding that although you did not have a stop sign or were required to yield that you did have time to either swerve or stop so that the accident did not occur.
With the last clear chance it typically means that the insurance company believes that the driver had the time and means to avoid the accident. The driver negligently failed to use that available time and means to avoid the accident. For example if you were approaching the intersection and though you did not have a stop sign saw that the other car was speeding and not going to stop in time than an insurer can say you had a last clear chance to stop and not allow the accident to occur.
For a couple of other examples of when reasonable care or last clear chance come into play, say your light turned green in an intersection and you proceed on though you see another driver is running the red light. An insurer may say you did not take reasonable care to ensure the intersection was clear before proceeding even though your light was green.
Or what if there is an accident with a person merging onto the freeway. The person entering the freeway is supposed to yield those already on the roadway however if the lane next the merge lane is open and the other driver failed to move over and make room than they may be found to have not taken a last clear chance to move over and avoid the accident from occurring.
Without knowing the specific details of the accident we cannot tell you why the insurance adjuster can to this conclusion about your situation however he should be able to explain to you how he found you to be 10 percent negligent and what last clear chance you had to avoid the collision.