ARES and RACES are the two names most often heard for organised amateur emergency communication, and they are different things. ARES, the Amateur Radio Emergency Service, is a volunteer group of licensed amateurs who have registered their skills and equipment to serve their community in an emergency. RACES, the Radio Amateur Civil Emergency Service, is a service defined in the FCC's Part 97 rules for civil-defense communication, run through government emergency agencies.
How they differ
Different organisers, same radio service. Many amateurs belong to both. Details differ by place, so ask your local group.
The practical difference is who you answer to. In ARES you are a community volunteer, and you typically support the organisations an emergency touches, such as a shelter, a hospital or a relief agency, by providing the radio link when phones and internet are down. In RACES you are part of a government emergency plan, so the agency decides who may take part, and certifies them.
Many amateurs join both, since the skills are the same: handling a net, passing messages accurately, and running a station from batteries. Which groups exist, and how they are organised, depends on where you live.
What members do
Train and drill. Regular nets, message-handling practice and exercises with the agencies they serve. See Nets and Net control procedures.
Know the system. Emergency responders use a common structure for organising an incident, and members are usually expected to understand its basics; see The Incident Command System.
Be ready to deploy. A charged go-kit, backup power and portable antennas let a member operate away from home for hours or days; see Go kits and emergency power.
Stay useful, not loud. Serve the agency's needs, pass messages exactly as given and keep routine chatter off the net; see Principles of emergency communication.
Getting involved
Get licensed and get a working radio. Groups differ in what else they ask for.
Ask your local club or emergency group which ARES or RACES teams cover your area, and how to register or apply.
Join their nets and drills before anything happens.
Complete whatever training your group asks for, and keep your equipment and skills current.
Specific requirements, structures and contacts differ from place to place and change over time, so ask your local group rather than relying on a general description.