About the obedience competition sport, where the dog is trained to perform a series of obedience exercices (heel work, scent discrimination, long duration downs, etc.).
However, it's not being used that way. Of the 46 questions using it, only the earliest one, Dog obedience scent discrimination, is unambiguously about the sport of canine obedience. One other, How do I teach my dog to jump over obstacles?, might apply because there are jumps in the higher levels of obedience competition (at least in the AKC version that I'm familiar with) even though the OP was more concerned with teaching their dog a skill than using that skill in competition.
The problem is that "obedience" means different things to different people. For people involved in the sport, it means the sport itself: "I'll be at the dog show next weekend. I've entered Fido in obedience and Rex in agility." For people uninvolved with the sport, it's the end-result of basic training.
I think a better tag for the sport would be obedience-trial (that phrase appears 94 times in the AKC Obedience Regulations so it will be familiar to practitioners), which opens its use to other animals and hopefully makes it clear that it doesn't mean basic training.
I also think that dog-obedience should be merged into the existing training tag (after retagging the 7 questions that use dog-obedience but not dog) since that's what the vast majority of the questions currently using it are actually about.