Context. The onset of star formation is intimately linked with the presence of massive unstable filamentary structures. These filaments are therefore key for theoretical models that aim to reproduce the observed characteristics of the star formation process in the Galaxy. Aims. As part of the filament study carried out by the Herschel Galactic Cold Cores Key Programme, here we study and discuss the filament properties presented in GCC VII (Paper I) in context with theoretical models of filament formation and evolution. Methods. A conservatively selected sample of filaments located at a distance D <500 pc was extracted from the GCC fields with the getfilaments algorithm. The physical structure of the filaments was quantified according to two...