Ionic solids are solids held together by ionic bonds. They are lattices composed of oppositely charged ions. Ionic solids tend to have high melting points ("high" generally being higher than metallic but lower than covalent). Because the electrons in ionic solids are localized (in the ions) these solids tend to be stiff and brittle like covalent solids.
As solids they do not conduct electricity (again because of the localize electrons). However, they do conduct electricity as liquids (or when dissolved in water) since then the ions can move.
Examples of ionic solids include NaCl and Ca(CO3). Ionic compounds are all generally found in nature as ionic solids.