The title itself gives a hint that it is a service. So ERS is a paid service from a classification society (Class) to perform engineering calculations in case of an emergency. Normally Class has expertise and resources to do such. The calculations use the electronic model of a ship and range from assessing damaged stability to substantiating strengthening of the hull elements.
For further detail I would suggest reading a post ERS: Managing emergencies, preventing disasters on DNV GL site. The post gives example of how it worked in case of a 14,000 TEU ship damaged after colliding with another ship in Singapore Straight.
