I am going through the training now, we have our practical-exercise/graduation this Saturday.
Most of it is pretty old stuff if you have been in the military. Some first aid, fire suppression/safety, organizing people/equipment, logging events/people/damage, triage, victim psychology, etc. You are supposed to help the Fire/Police gather information about the extent of the damage/casualties during a disaster along with helping out in other ways they might need. We also can be called upon to bring supplies (water/food/etc) to our local fireman if they are on an extended call during a non-emergency. All of this is completely voluntary and you don't need to worry about being "activated" or anything if you decide to just take the training and not go any further. They actually encourage people who have no intention of participating further to still complete the course as it helps prepare them to better react to an emergency of any kind.
CERT also does a background check and issues a photo ID good for a year. The ID gets you into areas off limits to other civilians during an incident. If you participate in further training/drill/events then you get ID renewed.
I figured it couldn't hurt to be on the inside in case of a disaster instead of just one of the huddled masses seeking relief. Not that I would actually be doing much huddling myself though.