the origin is the communist rule in Poland. Many people moved from rural areas to work in coal mines, steel plants and such. In their souls they were farmers, uprooted from their way of life. So the big industries bought land, parceled it and leased to the workers. Years later, the plots have been bought by the tenants.

Note: where I live, it's an urban area with ~2,5M people. The former "dirty" industries have been in many cases replaced by electronic factories, warehouses or IT/financial centers. The communal gardens still serve the purpose of giving city dwellers a taste of nature. For me personally, it's not appealing (my both grandfathers used to have one, one has been sold, the other is in the hands of my uncle), since I prefer to spend Saturdays hiking in the mountains. But for many people the gardens are the only form of outside activity.