What was the purpose of Roman Villas? Were they just for show like mansions of todays age?

by Torniquet-
DasImp

In short: it depends. It could have been a luxury estate, or a rich farm, or a very poor farm. It depends on region, and on when it was made vs when it was most active/prosperous. Below is an entry on Roman villas from the Oxford Classical Dictionary:

"Villa was the Latin word for a rural dwelling associated with an estate, and ranging in character from functional farms to the luxurious country seats of the elite (Varro, Rust. 1.11.1-12. 4.3.2.1-2. 18). Most of the literary evidence relates to Italy and primarily described farms run for the benefit of urban-based proprietors (Vitr. De arch. 6.6.1) though the most opulent seaside villas of the Roman aristocracy were sometimes built solely for pleasure. Aristocratic enjoyment of rural retreats and pride in creating architectural splendours there are well attested (Pliny, Ep. 2.17). The development of villas in different regions of Italy from the 2nd century BC is generally equated with the rise of latifundia (large slave-run estates), though these regions commonly exhibit divergent patterns of rural settlement and varied types of villa (from simple farmhouses to 'palaces'). Similarly the relative success and longevity of villas differed from one part of Italy to another: certain coastal areas famous for viticulture in the late republic had declined markedly by the 2nd century AD, whereas villas in some inland areas survived into late antiquity.

Provincial villa studies suffer from a geographical imbalance, with far more excavated and published sites in north-western Europe than from the Mediterranean countries. In peripheral territories such as Britain, where it can be exceedingly difficult to decide whether a particular structure would have been considered a villa by the Romans themselves, different criteria have been commonly used to define villas, encompassing aspects of Romanized construction or lifestyle (characterized by mosaics, painted plaster, hypocausts, baths, use of dressed stone and tile, etc.). Mediterranean-style peristyle houses are uncommon in Britain and Belgica), where winged corridor and aisled buildings tend to predominate, and other regions reveal their own characteristic styles. Important new approaches to villas in Britain look beyond their main Romanized buildings, to explore subsidiary farm buildings, field systems, pre-Roman and sub-Roman phases, and palaeoeconomic evidence for crops and livestock."