Like all comic book characters from the Golden Age, Giganta has had numerous origins stories throughout the years. In her first appearance, Giganta was a escaped gorilla who was captured by Wonder Woman and subjected to an experiment with an "electronic evolutionizer" (Ugh.). The experiment turns her into a woman.
Later, the new Giganta was Dr. Doris Zeul, a scientist diagnosed with an unknown blood disease which will soon kill her. When Wonder Woman is unconscious at the hospital where she works, Zeul abducts her and tries to use a machine she created to transfer her mind to trade bodies with Wonder Woman.
The transfer is interrupted, leaving Zeul's mind trapped in the machine. Her assistant manages to transfer Zeul's mind into the body of a gorilla named Giganta and finally into the body of a size-changing circus strongwoman named Olga.
With her new powers, Giganta begins working as a heavy-hitter on a bunch of supervillain teams, like Villainy Inc. and Gorilla Grodd's Secret Society. During that time, she's mostly portrayed as violent and bloodthirsty.
In 2006, Giganta returned with a new look in Wonder Woman's One Year Later storyline following Infinite Crisis. She teams up with Dr. Psycho and Cheetah to kidnap a friend of Wonder Woman's following her disappearance, demanding that she face them.
Then, there are her appearances on TV shows. In the "Superfriends" TV show, Giganta was a normal woman who stole magic dust from Apache Cheif and used it to gain the ability to change size.
Another popular incarnation of the character is from the animated Justice League shows. Though she only shows up in a few episodes, she does star in Issue 38 of the Justice League Unlimited comic book series. In the comic book, she joins the League to get closer to The Flash and goes on a rampage when he rejects her. I would say this is my favorite design for the character.
In her later appearances, Giganta seems to have reformed. In Warkiller, she runs into Wonder Woman. After a short skirmish, Giganta makes it clear that she is not looking to fight and that she is on her way to
a date with The Atom.
I especially like this scene between her and The Atom.