The Kaio-Ken is a powerful and useful technique that was taught to Goku while he was training with King Kai on King Kai's Planet. It is the most useful technique King Kai has at his disposal, as well as his signature technique.
In order to activate the Kaio-Ken, the user must shout "Kaio-Ken times 3!", with the 3 being interchangeable with any other number. When this happens, a red aura will quickly envelop the user while they take a fighting stance (sometimes not necessary).
When the Kaio-Ken is used, the user suddenly has very heightened senses. They get much more skillful in the power and speed areas so that they are able to increase their strength against whoever they are battling.
Goku has been seen using the Kaio-Ken against many of his opponents. The first instance that he needed to use it was when he was fighting Nappa during the Saiyan Invasion. During this time, he only used Kaio-Ken x3. However, he later used it against Vegeta in their battle for the Earth, and he used Kaio-Ken x4. This was the highest Kaio-Ken usage that had ever been seen during this time, and it was necessary for the Kamehameha to work and defeat Vegeta.
Later in the series, Goku was seen using it once more. This time, it was against Frieza. However, he had learned to use it in short bursts. This made it so that no normal being could see Goku using it, even Frieza. However, King Kai did recognize his usage of it, and he told the hopeful Tien, Yamcha and Chiaotzu that he had already used it to the power of ten.
Continuing their battle, Goku eventually used Kaio-Ken x20 in order to defeat the mighty overlord Frieza. However, it was not enough, and Goku was eventually forced to go into his Super Saiyan form that he had never used before.
While on King Kai's Planet, the dead Z-Fighters immediately started asking when they would learn the Kaio-Ken, the attack that helped save all of Earth from Vegeta. However, King Kai remarked that they would have to learn it in due time, for he had to help Goku.