Giovanni first appeared in Episode 15 Battle Aboard the St. Anne, he was shown on the television screen completely encased in shadow. (As seen to the left) This was the typical presentation of Giovanni up until the episode Battle for the Badge where he finally emerged into the light. The reason for Giovanni's presentation in this manner was to add a little air of mystery around him. Jesse, James, and Meowth were taking orders from him but it left the viewer intrigued. Who was this mysterious man? This "boss" they were talking to? What was his role? Why was he telling them to board the St. Anne? Giovanni as the enigma was rather a bright plot device to try and add that extra tension. Those who did not play the game would not recognize this man as Giovanni the gym leader, in fact, he was never addressed as such until much later on.
Giovanni in the Manga has a more intersting role, much like that of Giovanni in the game. He seems more energetic (IE: Not sitting in a chair petting a Persian 24/7) and he is depicted carrying out his own work rather than having his many minions do it for him. There are many interpretations of Giovanni over the different manga. In Pokemon Adventures he trails the hero pretending to be lowely fossil hunter. He not only is the Viridian City Gym Leader and the Team Rocket boss, he also is the controller of several other Gym Leaders including Koga, Sabrina, and Lt. Surge! His conspiracies know no bounds as he also attempts several experiments including the legendary Pokemon. He planned to form the three birds legendary birds into one Super Pokemon, he hunted the Legendary Deoxys, and let's not forget his exploits with Mewtwo. It is also revealed in the Manga that the rival, Silver, is his son and he plans for him to one day take over Team Rocket. (This, however, is never said in the games or in the anime, so is only a storyline of Pokemon Adventures.)
In Kagemaru Himeno's series, How I Became a Pokemon Card, there is a short story about how Giovanni met his Persian. He came across an injured Persian that was being hunted for its rarity and fine, silky fur. It was a touching story of how Persian was rescued and explains why Persian is always at his side.