Cellars are very common, most houses have one. But there are differences. Some cellars from the middle ages are really huge and have an interesting story. That is the sort of cellars, predestined for showcaves.com. We will not list your basement, don't panic.
Some cities are built on soft rocks, like sandstone, tufa, or travertine. Those rocks are so soft, sometimes it is even possible to dig a hole using a pickaxe and a shovel. Travertine is cut with a saw, as long as its still underground and humid.
Often, there is a second benefit in building a huge cellar: the removed material may be used for another purpose, building houses, sand for mortar or for cleaning (as an abrasive). So many cellars are actually former quarries which were reused.
Cellars were used to store all goods which must be kept cool to stay fresh. This works with most food, especially vegetables, potatoes, roots, and more. Also it is possible to store many different things together. There is normally no need to keep them separated. Nevertheless there are some specialized cellar types, which were built and used for just one purpose.