It is the mental and physical perfection of the core Super Saiyan form
Whether there are intended to be differences in a Full-Power Super Saiyan's facial features from those of a standard Super Saiyan is debatable. This can be evidenced by a regular Super Saiyan's facial expressions carrying a very stern look whether or not this complies with the emotion they are feeling, while a Full-Power Super Saiyan's facial features are more similar to their base form. This however could be due to the fact that the Super Saiyan has reached a state of peace and the fierce amount of emotions is not needed to transform. The Saiyan's aura also changes, and takes a more relaxed, flowing motion rather then the original violent flame-like appearance. The Full-Power Super Sayian's hair is more detailed and somewhat brighter.
"The Balance of Power", when Goku witnesses and experiences the substantial flaws of the advanced Super Saiyan stages. Goku decides not to train again to defeat Cell, but rather to spend the time having a common life in Super Saiyan state to control that transformation without becoming weaker, as complete mastery of the original Super Saiyan form is the best way to advance his abilities, and ultimately achieve greater power. As a result, he focuses on training his body to suppress the negative effects of the Super Saiyan form, such as ki consumption and personality alterations. This state could only be achieved in a much less strenuous manner than Vegeta and Future Trunks' forcible attempts to advance.
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 transformation 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 of ki can thus be focused into the attacks giving the user access to power greater than that of even an Ascended Super Saiyan.
The key to the Full-Power Super Saiyan 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 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 second and third stages of Super Saiyan are rendered obsolete.
Goku and Gohan are the first to achieve this state while spending time training in the Hyperbolic Time Chamber. During Cell's tournament, Goku battles Perfect Cell in what seems to be an even fight, with no apparent advantage on either side. Eventually, Goku forfeits the match and has Gohan step up in his place. Cell initially has an advantage over the young Super Saiyan, mostly because of Gohan's gentle nature and thus his refusal to go all-out, and begins to intimidate Gohan into utilizing his full strength (something Goku was counting on when he ended his own fight). After 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 wasn't until Cell killed the peace-loving Android 16 that Gohan lost all self-control over himself and transformed into a Super Saiyan 2.
Later in the Other World Tournament, Goku becomes victorious in his fight against Pikkon while in a full-power state. In the film Broly: The Legendary Super Saiyan, Goku and Gohan battle Broly in this state (chronologically this is the first time the form was used in battle), only to be badly beaten by the Legendary Super Saiyan. In the film Bojack Unbound, Gohan again fought using in full-power, only to transform into a Super Saiyan 2 afterward and defeat Bojack and the Galaxy Soldiers.
Because Full-Power Super Saiyan 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.