An example would be if you'd applied blends/fillets to an object and then suppressed them, the object would then revert to having its edges. You might need an edge to work a dimension or another feature off, suppressing the blend can give access to it without having to delete or undo the entire object creation. In other circumstances, it can preserve an object's associativity to its creation history and permit rebuilds without crashing the object or dissociating it from, say, a sweep's profiles and guides. You can step into an object's history and perform actions on it while suppressing dependencies, for example if you've got successive features where a fillet is created, then a subsequent one that blends into it, the later one is dependent on the earlier, but you can suppress the earlier one and redo it with a different radius without having to undo the later, which is useful many afterthoughts later.
To suppress, select an object and invoke Concept Explorer. In the 'features' tab, there's a history tree with a trunk that branches to features, the ends of the branches are dependent on the connections to the trunk, which grows either from generators (profiles, guides, rails) or primitives. Right-click on the branch features and appropriate (contextual) options are offered, suppression is one of the options.

You add features to objects as you build them, so options are contextual. I'm assuming that when you say 'solids', you mean primitives (blocks, ellipsoids, cones, etc), and assemblies of primitives as parts. Primitives are essentially featureless, only their sizes are variable.