Dog training collars are a training aid that help you teach your dog to follow commands or to modify a behavior. The collar allows you to provide the dog with instant feedback, providing a positive stimulus to reinforce positive behavior, and a negative stimulus to deter negative behavior. Used in conjunction with a structured training program, a dog training collar helps you more effectively teach a dog, and results in a greater recall than other training methods.
The dog wears a training collar, and the trainer holds a receiver that can control the collar. Depending on the system, the trainer can produce a warning tone, a reward tone, or a correction (static shock, citronella, vibration ultrasonic sound, etc).
In a typical training protocol, you will first teach the dog the desired command or behavior, providing a lot of repetition so the dog knows exactly what they are supposed to be doing. In the early stages of training you will use primarily positive reinforcement to shape the behavior, conditioning the dog to associate obeying the command with some positive outcome such as their getting a treat or praise. Once the dog is confident with the command, you being layering on the correction when the dog is willfully disobeys the command. This negative reinforcement teaches the dog there is an unpleasant consequence for disobedience.
Both professional trainers, and studies agree that a training regimen that uses both positive and negative stimulus results in faster learning, and learning that is more robust. Positive stimulus keeps dogs enthusiastic about training, but dogs don't always obey, particularly when there is some high excitement temptation to disobey (e.g. they see another dog at the park and dash off, or they find food on the ground and eat it). Negative stimulus results in higher compliance, but overused can diminish the dogs enthusiasm for work. Used together positive and negative stimulus balance each other out, and produce a better trained dog.
A training collar is helpful as part of the training process because it is a way to instantly give a dog either positive or negative feedback in real world conditions. When you are training a dog off leash, or doing field work where your dog can be anywhere from a few feet to a few miles away, a training collar helps you communicate to the dog at the exact moment they did something, allowing you to reward good behavior (with a praise tone) or halt bad behavior (with a correction).