Since the 1950s, clicker training (or more appropriately "click-and-treat" training) has grown popular with animal trainers across a spectrum of species, from dolphins to horses. The main reason for this is that clicker training is humane, compared to earlier methods.
Prior to the clicker training concept, animals were trained primarily through a combination of negative and positive reinforcement. In other words, an animal was punished, often with pain, for not performing in a desired way. If an animal did the trick or performed a behavior to satisfaction, he was rewarded with food, praise or the absence of punishment.
During World War II, this "punishment" method appeared to be the fastest way to teach animals to perform for the war effort. After the war, army trained "behaviorists" and animal trainers carried the practice over to civilian life. But when it came to training dolphins or killer whales, the technique was virtually impossible to perform. It was not possible or practical to "punish" a dolphin or killer whale swimming in a tank. Trainers needed to be able to "mark" a desired behavior, even when they couldn't reward the animal immediately.
Because aquatic mammals have highly developed hearing, using an auditory signal that meant "That's right!" made sense, and the initial signal was a blast on a whistle. The whistle blast had earlier been paired with something the dolphin would value as a reward – a fish treat. So when the dolphin heard the whistle, not only would he know he'd done what his trainer wanted, but he also knew he would be rewarded with a fish. He would go on working through a number of behaviors, limited only by the inventiveness of his mind, until he hit on the one which the trainer desired.
Undesired behaviors were not punished (he wasn't smacked on the beak, for instance); they were simply ignored. No one was making him try new behaviors by applying negative reinforcement; he was working because he was determined to find out what would get him his fish treat. Once he figured out the desired behavior, and performed it consistently, the trainer could pair a verbal command just before the behavior, so he'd know what was wanted at any given time. More complex behaviors could be broken down into small pieces and these later combined to get the whole "trick."
Learning became a fun, intellectual, win-win exercise. Once trainers of other species saw the benefits of positive reinforcement (rewarding only the desired behavior) and operant conditioning (pairing a signal with a reward so that the signal alone confirms the animal did what was wanted) this type of training began to spread.
One big change from the early marine mammal training is the type of signal used to affirm that the animal is doing the right thing and a reward is forthcoming. Clickers have come to replace whistles as the favored signal for non-marine mammals. The sound is novel, something the animal is unlikely to encounter in everyday life and yet it carries well so that a horse can hear it even across a crowded arena. Most animals do not find the sound scary and for those few that do, muffling the clicker with a little duct tape helps the animal accept it during training. Later the duct tape can be peeled away until the full click is accepted.
However, there is nothing special about the clicker. Any novel sound can be used provided it can be made quickly and consistently and be heard by the animal being trained. Some trainers prefer to use their voice to trigger a successful response. There is nothing wrong with this, except that most of us do not have the focus without the clicker in hand to use the same word consistently, one the animal hasn't heard repeatedly and meaninglessly, in the same tone of voice at the exact moment every time the animal performs correctly. The clicker is very clear; the voice carries too many inconsistencies for most of us.