We present a large sample of fully self-consistent hydrodynamical Nbody/Tree-SPH simulations of isolated dwarf spheroidal galaxies (dSphs). It has enabled us to identify the key physical parameters and mechanisms at the origin of the observed variety in the Local Group dSph properties. The initial total mass (gas + dark matter) of these galaxies is the main driver of their evolution. Star formation (SF) occurs in series of short bursts. In massive systems, the very short intervals between the SF peaks mimic a continuous star formation rate, while less massive systems exhibit well separated SF bursts, as identified observationally. The delay between the SF events is controlled by the gas cooling time dependence on galaxy mass. The observed global scaling relations, luminosity-mass and luminosity-metallicity, are reproduced with low scatter. We take advantage of the unprecedentedly large sample size and data homogeneity of the ESO Large Programme DART, and add to it a few independent studies, to constrain the star formation history of five Milky Way dSphs, Sextans, LeoII, Carina, Sculptor and Fornax. For the first time, [Mg/Fe] vs. [Fe/H] diagrams derived from high-resolution spectroscopy of hundreds of individual stars are confronted with model predictions. We find that the diversity in dSph properties may well result from intrinsic evolution. We note, however, that the presence of gas in the final state of our simulations, of the order of what is observed in dwarf irregulars, calls for removal by external processes. Appendix A is only available in electronic form at http://www.aanda.org