They are a couple of demons or devils, in hell. Their demon dog is on fire, which is probably a common occurrence in their firey realm, therefore someone needs to “put the dog out,” which is a play on words–put out as in extinguish the fire. As opposed to a similar scene which would be a normal couple in their living room, and the wife says it’s husband’s turn to “put the dog out,” as in, let the dog outside. It’s all an absurd pun.