In "Anathem," the avout (fraa and suur) used "spheres" to do various things. The spheres wered used as a tool to make life comfortable in most cases, but what are they exactly? How should I visualize them? Stephenson didn't really paint a clear picture of it.
It is hard to describe a visual image of the spheres, simply because their forms were so malleable.
The sphere is a porous membrane. Each pore is a little pump that can move air in or out. Like a self-inflating balloon. The spring constant - the stretchiness - of the membrane is controllable. If you turn the stretchiness way down (that is, make it stiff) and pump in lots of air, becomes a hard little pill.
You can also do the opposite, and make the membrane very stretchy, and or/remove most of the air.
So the sphere can look like anything from a small, hard ball, to a large, floppy disk, plus anything in between (in the passage that follows the above quote, fraa Erasmas makes his sphere into a flat mat, and then inflates it into an air bed between two and three feet in diameter).
In another reference, it can be shrunk to a size that fits easily in the palm of a hand.
The whole thing is a geometric metaphor. Think about it: you have the "bolt" which is a flat sheet, basically a cartesian plane. Then you have the "chord", which is a rope, or a platonic line, and then you have the "sphere", which is a sphere.
It has some practical applications (as you see in the book), but it's mainly symbolic.