Can someone explain to me exactly what a game editor does.
A game editor or level editor allows you to place objects within your world like trees, houses, skybox and terrain. If you ever played Dark Cloud you earn "objects" and can place them within the towns in real-time. A game editor gives you complete control over every object in the game. It would be harder to place objects by just entering their 3D coordinates manually. Here are some editors for example IRREDIT which is used for the IRRLICHT game engine also Torque has a nice editor too.
How do you incorporate the game script into the editor
A game script is were most of your logic comes into play. The game script allows you to change things without having to recompile your game code. How this gets loaded into the game is up to the game engine.
how exactly would you go about scripting one?
I would recommend finding a game engine like Torque or OGRE3D and read the tutorials and documentation they have for you. Even though it might seem boring I would start off making simple games like PONG, TETRIS or Tic-Tak-Toe. Then work your way up to FPS, RPGs and Fighter Games.
You can find the websites of some game engines below