A cinder is a small, hot, glowing coal from a fire. When you put out a campfire, it's important to make sure that not one single cinder remains.
It's easy to miss the fact that a cinder is still hot, since it remains that way long after every flame has been extinguished. When people clean out their wood stoves, they put the ashes in a metal bucket — rather than a flammable paper bag, for example — in case there are hot cinders hidden inside them. The word cinder comes from the Old English sinder, or "slag." The c comes from the otherwise unrelated French cendre, "ashes."