CERA (Catastrophic Emergency Response Agency) is a federal agency which was created to deal with large-scale natural disasters. In Tom Clancy's The Division, they are the group most focused on halting and containing the spread of the Green Poison virus.
Before the Game
CERA was created to help deal with large-scale natural disasters, when the situation was overwhelming local and state relief efforts. It can be assumed that CERA was also in New York when Hurricane Sandy hit (since the former has been mentioned in the game several times over).
During the First Wave
When the First Wave of Division agents was deployed, CERA was in charge of all field hospitals, treatment centers, Safe Houses and supervised the construction of the Dark Zone. They also employed volunteers to help them ration out food and supplies to civilians in need. Vehicles (from cars to transport CERA officials to shipping eight-wheeler trucks) can be found all over the New York City and were used to adequately deliver much-needed supplies.
However, food, medical, and personnel shortages led to increased riotings, to the point where the Joint Task Force (who were in charge of protecting these supplies and personnel) couldn't handle it. After the major disaster of the Dark Zone, along with the First Wave Division agents going MIA, forced CERA to pull out along-side the JTF, and CERA support from all hospitals and treatment centers are no more.
New York Collapse
In New York Collapse (an Interactive novel based on the Survival Guide in game) there is a yellow sign from CERA stating that they'll be in the neighborhood vaccinating everyone against smallpox. This is before CERA lost their grip on supply delivery, and before they discovered that the smallpox strain was heavily mutated, rendering the vaccine useless.
CERA has been incredibly weakened at this point, with very little manpower. However, despite this lack of manpower, CERA still continues to treat the sick and research for a cure along side local doctors and nurses, although this research and treatment is limited to those who stay in the Base of Operations and some Safe Houses.
Unlike the JTF, CERA has no role, gameplay-wise. They mostly operate in the background, usually requesting agents to collect data during Encounters, and play a bigger role than usual during the mission Hudson Refugee Camp, where both CERA and JTF doctors and soldiers who are first aid-certified arrive on the scene to take blood samples from the survivors.
CERA workers can be found in the Base of Operations (usually in the Medical Wing) treating sick or wounded JTF soldiers and/or civilians, and can be found in a few safe houses.
Real Life Counterpart
The real-life counterpart of CERA is FEMA (Federal Emergency Management Agency), as both are federal agencies that are dispatched when local and state relief efforts have failed or been overwhelmed from natural disasters. Their logos are also similar when compared.