Primary reinforcers are anything that you don't have to teach the dog to like at first. That is all it means. A common misconception that people have are that primary reinforcers are the best to use because they are primary. Most primary reinforcers relate to the basic survival needs of the animal. For example: food, water, comfortable places to lay on, bladder relief, sniffing, chasing moving objects, vocalizing, attention, etc. They can be very basic, but the rule is that you don't have to teach a dog that sniffing the ground is a fun activity. The degree to which dogs find these activities pleasant, especially the hunting behaviors, is due in part to genetics and dog trainers call it drive. I will reserve this for a later topic.
Secondary reinforcers is anything that can predict a reinforcer. Basically, it is anything that you have taught your dog to like. They are also called conditioned reinforcers. Conditioned reinforcers can be much more reinforcing to a dog than primary reinforcers. A human example of a secondary or conditioned reinforcer is money. Most people, if given the choice, would choose to be rewarded with money than anything else. In order to maintain the value of a secondary reinforcer, you will have to continue pairing it with something that is reinforcing. Following the human example, imagine if you had a lot of money, but suddenly, nobody took your money any more. You would not find money to be valuable. This is also the case with dogs. The clicking sound of a clicker or a bright "yep" being used as a marker word is the canine equivalent of money. Most secondary reinforcers are closely tied with primary reinforcers so that they do not lose their value. I will list an example now, using my own dog:
Oats loves his stuffed animal. A stuffed animal is not a primary reinforcer, but a secondary one that is reinforced with chasing and catching and holding the item in his mouth. It is also tied to attention from me. All of these things are primary reinforcers. I didn't have to teach Oats to enjoy chasing things that moved like prey, or enjoy holding them in his mouth.
Now, a tertiary reinforcer is anything that reliably predicts the chance of receiving reinforcement. They are, technically, still secondary or conditioned reinforcers because they still predict a reinforcer, but are called tertiary reinforcers to describe how far removed they are from the primary reinforcer. Cues, in clicker training, are a good example of a tertiary reinforcer. The reason they become tertiary reinforcers is because the cue is a discriminative stimulus that says "okay, the chance to receive reinforcement is on." This is where the term poisoned cue comes in. This means that the cue cannot be a tertiary reinforcer because the cue no longer means "okay, the chance to receive reinforcement is turned on." Instead, the cue signifies a scenario where the dog can either receive punishment or reinforcement. This is why the cue is no longer reinforcing. If your dog has a favorite trick that he will do anything for the chance to show it off, if you will only say the word, then that is a tertiary reinforcer.