Breakaway collars are pet collars that fit around the neck and have a clasp that will unlatch with pressure. They are meant to prevent injury in the case your pet becomes stuck on an object.
Note that there is some controversy over the safety of using breakaway collars on cats. The Journal of the American Veterinary Medical Association apparently conducted a study in 2010 that determined simple buckle collars are the best choice for cats, but I can't find a link to the study. Most of the recommendations on other pet websites call breakaway collars the safest option, but I wanted to note that cat owners should do their own research on which collar is best for each situation.
When our Timmy and William were kittens, we used small breakaway collars (one blue and one orange) to help tell them apart as we got to know them. We no longer use collars for any of our indoor cats; they are chipped and under strict control in the case of travel (to the vet, cat hotel, etc). We do have harnesses available to use and if we had to leash up the boys for any reason, we'd use them rather than any kind of collar.