In the World of Goo, the geometry objects are what make things solid. Geometry is what the Goo Balls can sit on, walk on, attach to, bounce off etc.
There are several different kinds of geometry object you can include in your level, but no matter how complicated your level is, it's all built out of very simple shapes (rectangles and circles).
Geometry objects can be fixed in space (static) or moveable/moving (dynamic). They can be made of various materials, and can have a whole host of different effects on the balls and other things.
Geometry objects can also have images attached to them. This is unnecessary on static geometry - it is usually simpler to use a separate SceneLayer item for the image. But if you want the geometry to move, and you want the image to move with it, you must add the image to the geometry object.
Geometry IDs
Every geometry object has an id attribute. When you add a geometry object to your level, WoG Editor will automatically assign it a unique id of the form geometry{number}.
You can change these IDs to whatever you like, and the game is quite flexible in that regard. It will allow objects with duplicate IDs and blank IDs without complaint. However, this can cause you endless problems whilst you're editing the level.
WoG Editor will report any problems by refering to an object's ID. If you have many objects with the same (or blank) ID, you won't know which object actually has the problem.
Once you start designing larger levels, with dozens or hundreds of geometry objects, it can be useful to start giving them "meaningful" names: platform1, leftwall, killerwheel or whatever. As long as you keep these names unique, you will be fine.