A hard discount (short form of "hard discount store") in Europe is a mini-supermarket specializing in cheap prices.
Hard discounts sell only stuff from unknown brands. They do not favor the local market, preferring to get whatever is cheaper in Europe. They have very little variety, normally there is only one brand of canned tuna, one brand of toilet paper, one brand of cereal. The core of their offer is non-fresh food, even though certain shops, probably desiring to become more a one-stop solution, have started offering a small fresh food section, including bread and vegetables.
This type of store achieves economy also by reducing staff to the core; this implies that the goods are not placed on shelves, but they are often left in the original shipping carton that is is simply ripped open and left on the shop floor. As the shop is typically run by two or three people, there are often queues at the checkout.
A hard discount store is always either owned or franchised from a chain. The biggest in Europe is probably LIDL; of German origin, it started operation in the thirties, but it expanded to European size in the '90s. Other chains are Eurospin, Ed, Aldi and Dico, with different degrees of presence depending on the country.
And are the prices good? Yes, they are. Once you accept the limits of this type of outlet, you can have significant savings. There is also a certain pleasure in thumbing your nose at large brands. Hard discount chains account for approximately 8% of the European retail food market.
See also: the excellent writeup on Aldi; many of their principles apply to all hard discount stores.