If, through misfortune, you have to make a claim on your home contents or buildings insurance, a loss assessor will work for you to put a value on the damage caused and present your case for compensation to the insurance company.
The argument for using one is that as professionals they know how to get what you're due and to prevent an insurance company from taking advantage of you (not that they would!)
In short a loss assessor is on your side, while a loss adjuster is working for the insurer.