From Bulbapedia, the community-driven Pokémon encyclopedia.
Team Rocket executives and administrators are, as their title suggets, high-ranking members of Team Rocket. In some cases, they are subordinates of Giovanni, but upon his absence, they become the leaders themselves.
In the games
Like Team Rocket Grunts the Rocket Executives and Admins are considered as a Trainer Classes. They are the rulers of Team Rocket when Giovanni is gone.
There aren't any distinct Rocket Executives in Generation I but in Pokémon Yellow there are two Team Rocket members called Jessie and James which appear to be Executives or more like "something higher than grunts". They are guarding Giovanni in Celadon Hideout and Silph Co..
Fire Red/Leaf Green
In the Sevii Islands, the Rocket administrators face players before they battle Scientist Gideon. After defeating the male administrator, he sees the players' Earth Badge and realize that the Viridian-based Team Rocket has disbanded; he then tells the players that he will find Giovanni and revive Team Rocket.
It is very likely that the Rocket administrators are the same people as the Rocket executives in Gold/Silver/Crystal, as hinted by the similary in their teams. Further clues include the male administrator's determination to revive Team Rocket after you defeat him in the Warehouse, as well as the information given on the computer screen which the Rocket administrator was working on (it says "The influence of magnetic waves on Pokémon evolution"). This is linked to what happened in Gold/Silver/Crystal, when Team Rocket used magnetic waves to drive Pokémon, such as the Red Gyarados insane.
In a money-making scheme, the Rocket administrators send grunts to the Slowpoke Well to harvest the tails of Slowpoke to sell. Later, the Rockets build a base near the Lake of Rage that utilizes a high-frequency sound that influences Pokémon evolution, then in one last try to contact Giovanni they and the grunts take over the Goldenrod Radio Tower. Players fight and defeat administrators at both the Lake of Rage Hide Out and the Goldenrod Radio Tower. When the final Rocket executive is defeated, he announces that he will disband Team Rocket, as Giovanni did three years ago.
Jessie and James
Fire Red/Leaf Green
Rocket Administrator, female
Rocket Administrator, male
In the anime
It is unknown whether or not there are executives as present in the games and manga, as Giovanni is still in control of the organization. Instead, the anime tends to focus much more on higher-ranking Team Rocket members such as Domino, Vicious, Annie and Oakley, who are warriors rather than administrators.
In the manga
Lt. Surge, Koga, and Sabrina are Team Rocket executives. Blaine, previously an executive, left the organization because of problems with Mewtwo. In the Yellow saga, the executives were recalled by Giovanni after he saw a battle between Lance and Yellow and realized he still had much to learn.
Executives are replaced by two sub-leaders, Charmaine and Keane, while the real Leader is Mask Of Ice. Their designs are based on Executives from games.