A Geometry object can be made fixed and unmovable by setting its static attribute to true.
Static objects are used for Walls, Cliffs, Platforms and the other things in your level that will never move. The vast majority of the geometry in your level will usually be static, so WoG Editor sets static=true on geometry objects when you add them.

The static attribute only affects the "fixed" nature of the Geometry object, it can still be assigned a [material] and tags.
You can also apply images to static geometry, however you are normally better using a separate image object. The only time that static geometry requires an image is when it can be destroyed - see [Making Geometry less Solid]

Note on Building Walls and Cliffs

There is a bug (more a "weakness") in the World of Goo game engine which allows fast moving Goo Balls to pass through thin walls. This has been used to great advantage by many players in order to beat levels faster or better.

However it can also be annoying and problematic if a level is designed "poorly" and Goo Balls can accidentally pass through thin walls and become stuck or die. The best way to avoid this problem is to make your geometry as big and solid as possible, rather than building thin walls around the edges of the images. Overlapping regions are fine, in fact they are encouraged, since Goo Balls can get stuck in small gaps between geometry that almost touches.