Dwarf galaxies, as the most numerous type of galaxy, offer the potential to study galaxy formation and evolution in detail in the nearby universe. Although they seem to be simple systems at first view, they remain poorly understood. In an attempt to alleviate this situation, the MAGPOP EU Research and Training Network embarked on a study of dwarf galaxies named MAGPOP-ITP. In this paper, we present the analysis of a sample of 24 dwarf elliptical galaxies (dEs) in the Virgo cluster and in the field, using optical long-slit spectroscopy. We examine their stellar populations in combination with their light distribution and environment. We confirm and strengthen previous results that dEs are, on average, younger and more metal-poor than normal elliptical galaxies, and that their [α/Fe] abundance ratios scatter around solar. This is in accordance with the downsizing picture of galaxy formation where mass is the main driver for the star formation history. We also find new correlations between the luminosity-weighted mean age, the large-scale asymmetry, and the projected Virgocentric distance. We find that environment plays an important role in the termination of the star formation activity by ram-pressure stripping of the gas in short time-scales, and in the transformation of discy dwarfs to more spheroidal objects by harassment over longer time-scales. This points towards a continuing infalling scenario for the evolution of dEs.