Full-Power Super Saiyan (超サイヤ人フルパワーSūpā Saiya-jin Furu Pawā) is the complete mastery of the Super Saiyan form, completely unrelated to the Ascended and Ultra stages of the transformation. Instead, it is a state of mental and physical perfection of the core Super Saiyan state itself. The idea is thought up by Goku, who insists he and Gohan use it, which they do to great success.
In the real world, athletes who train in aerobics for extensive periods of time experience heightened states of rest: heart and respiratory rate are much lower than that of a normal person. The Super Saiyan form follows a similar fundamental concept: by remaining transformed for extended periods of time, the Super Saiyan can desensitize themselves to the negative effects of the transformation. Their wild emotions are kept in check, resulting in a more strategical fighting style, and ki consumption is reduced to negligible amounts. Energy radiation is reduced in tandem, and the aura takes on a smoother, flow-like appearance. By mastering the transformation, the Super Saiyan is able to retain transformation almost subconsciously. In requiring less ki to contribute to maintaining the transformation itself, the maximum amount ofki can thus be focused into the attacks giving the user access to power greater than that of even an Ascended Super Saiyan. Vegeta notes the incredible side effects of the transformation by stating "They look like Super Saiyans... but I don't feel the energy...! It's like... it's their natural state...". It is a really cool power.
The key to this state is energy conservation rather than boosted energy output. This results in a Saiyan who is able to fight longer and more efficiently than with the Ascended and Ultra stages of Super Saiyan, and can even remain transformed for days without powering down as long as they don't expend too much energy, essentially making the transformation the Saiyan's base form. Following the creation of this concept and the introduction of Super Saiyan 2, the Ascended and Ultra stages are rendered obsolete. Because the Full-Power Super Saiyan form was a learned state of being, and not necessarily a typical transformation or power stage, it was used throughout the remainder of Dragon Ball Z by Goku and Gohan.
Whether there are intended to be physical differences in a Full-Power Super Saiyan from those of a standard Super Saiyan is debatable because most of the physical differences can easily be explained as changes in Toriyama's artwork as the series continued. The only confirmed difference is that the Saiyan's facial features exhibit less tension and ferocity than the regular Super Saiyan form, which can be explained by the mastery over the ki consumption and the emotional restlessness that the regular Super Saiyan transformation causes. The aura is also noted to be different. Whether or not it was by accident, the aura is also seen to be less violent than the second and third grades of the Super Saiyan, but not as gentle and flame-like as the original form as seen in the manga series. When relaxed, the user's hair appears more of a yellowish white, but when powered up, the golden glow seen often in the first transformation makes a return.
Goku and Gohan were the first to achieve the Full-Power Super Saiyan state while spending time training in the Hyperbolic Time Chamber, in which Goku realized they must "... work on getting rid of that instability... that restless feeling.", in a sense, regular Super Saiyan must feel like their normal forms. They spend the remainder of their time within the chamber and ten days before the Cell Games maintaining their Super Saiyan forms until they felt relaxed, a mastery of the Super Saiyan form. After having achieved this mastery, Goku and Gohan were able to freely modify their power levels as they would in their base forms. Their bodies' familiarity with the transformation also enabled them to reach their maximum Super Saiyan powers with no adverse effects present in the Ascended and Ultra forms.
The form was first seen during the Cell Games, Goku battled Perfect Cell in what seemed to be an even fight, with no apparent advantage on either side. Goku eventually forfeited the match and had Gohan step up in his place. Perfect Cell initially had an advantage over the young Super Saiyan, mostly because of Gohan's gentle nature and thus his refusal to go all-out, and began to goad Gohan into utilizing his full strength (something Goku was counting on when he ended his own fight). After Perfect Cell unleashed seven Cell Jr. clones of himself to attack the Z Fighters, Gohan withstood less and less of the torture and his anger began to rise. It was not until Perfect Cell killed the peace-loving Android 16 that Gohan lost all self-control and transformed into a Super Saiyan 2, allowing him to defeat the Cell Jrs. and later Perfect Cell.
The Full-Power Super Saiyan form would be used by Goku and Gohan for the remainder of the series as their norm for transforming. However, they would usually have to transform into a higher state in order to combat the more powerful foes, such as Majin Buu. Vegeta seems to have later learned this, and Goten and Trunks also seem to be very relaxed when turning into Super Saiyans, very calm also.