I tell people solid modeling is making a real part in the computer. The part is 3 dimensional, has volume, and mass rather than a bunch of lines drawn 2 dimensionally in multiple views to represent a real part with volume and mass.
Solid modeling is simply a set of macros that automate the surface creation, trimming, joining functions, typically using boolean operations which are transparent to the user, and a rule: a volume definition must be maintained throughout serving as an integrity check. An arbitrary density can be associated with the volume definition for mass calculations.
I just tried that on my mother, she now has one very strange blank look on her face. Unfortunately my ma doesnt quite grasp computers yet! ( she doesnt even know who Pac-Man is!!!). Laser guy pretty much simplified it as much as possible, it is also how i would normally describe solid modelling.
As I understand it, Pro/E is a boundry representation modeler (B-rep) as opposed to a Boolean modeler. I don't think it makes a bit of difference but used to be a point of hot contention back when Pro/E was the new kid on the block. Pure boolean systems only use the intersection of simple primative shapes like spheres, cubes, torroids, etc. I don't think there is a pure boolean solid modeler left. None of this matters to the end user or to the definition of solid modeling.
You gents are correct in a strict sense and certainly correct as to relevance. If I were to guess what's happening behind the curtains, though, when creating any of the solid base features it goes something like: the feature is created as a discrete solid, intersections found, surfaces split, appropriate surfaces discarded and finally the remaining quilt stitched into the existing solid body. Essentially a boolean operation.
Re accuracy... it is relatively simple to find accurate intersections between analytic or primitive surfaces but doing the same for higher order surfaces is not a job for the faint-hearted or casual developer. Even more so dealing with fuzzy tolerant edge intersections. I think that may be what was abandoned.