The character has been used in different ways as relates to John Carter.
Her first appearance was in Four Color #437. As each version of the character is different and by different publishing companies, every incarnation of the character could be considered to be her first appearance.
Major Story Arcs
Thuvia was a princess of the kingdom of Ptarth. At some point, she was captured by the Thern and taken to Valley Dor. Made a slave, she was forced to service the depraved needs of the Thern, Sator Throg. After having his advances repulsed one time, he throws Thuvia in a pit with Banths as punishment. Unexpectedly Because she had a pet Banth once, she manages to sooth the savage beasts and control them and bemused by this, Sator keeps Thuvia alive long enough for her to be rescued by John Carter and Tars Tarkas. She helps the heroes escape the Thern slave pits and finds Sartor along the way, avenging herself for the many indignities she suffered. Thuvia develops an infatuation for Carter after he rescued and comforted her, going as far as declare her love for him.
When Carter gets split from the Tarkas and Thuvia, she is later recaptured by the First Born and imprisioned with none other than Dejah Thoris, John Carter's own wife, to whom she reveals he has returned to Barsoom and Thuvia is madly in love with him. The two Red women imprisoned within the Temple of Issus for a year alongside a Phaidor, a Thern princess who was also in love with Carter, emerging only to fall directly on Matai Shang's hands, who wanted revenge against John Carter for ruining the worship of Issus. However, Shang is betrayed and killed by one of his allies, Salensus Oll, who takes a liking to the women and declares they shall be his concubines. The tables turn quickly however as an Red Martian force sieges Oll's stronghold and the three women take the opportunity to stab him to death.
Thuvia is finally freed and returns home, and its hinted she takes a liking to Carthoris, John and Dejah's son.
Her physical appearance tends to vary between the books and comics - while her looks are not described in detail on the source material, its established she is an Red Martian and therefore many artists depict her similarly to Dejah Thoris, as having black hair and reddish skin tone. However, many official cover illustrations for the books have strangely depicted her with blonde hair and light skin, which is usually associated for White Martians.
As with many females in Barsoom, she wears very revealing clothing, only instead of jewelry and gold ornaments, she wears two-piece slave bikinis in her Dynamite appearances, having spent most of her past and screen time as a prisoner.
Powers & Abilities
Like all Martians, Thuvia displays low-level telepathy and psychic powers. She is able to communicate the Martian beasts known as Banths ever since her captivity among the Therns. Thuvia can command them to stop, turn docile or aggressive at will which is manifested as some strange language within dialogue. This is not a ability she can explain or understand very well, its simply something she can do naturally.
Thuvia is likely still an young woman by Earth standards, its possible she had stopped aging after that physical maturity as with the rest of Mars.