an inorganic, nonmetallic solid

This mouthful is the backbone of the definition of a ceramic, three words that each rule something out. 'Solid' rules out liquids and gases; a ceramic holds its shape. 'Inorganic' rules out the carbon-chain compounds of living things and plastics (organic chemistry); ceramics are built mostly from metals joined to nonmetals like oxygen, nitrogen, and carbon. 'Nonmetallic' rules out the metals themselves, copper, steel, aluminium, whose loosely shared sea of electrons makes them shiny, bendable, and conductive.

More carefully: inorganic means not based on carbon-hydrogen chains, though carbon itself, as in silicon carbide SiC or even diamond, is counted as ceramic-like. Nonmetallic means the bonding is ionic and/or covalent, not metallic; the electrons are pinned to particular atoms rather than roaming freely. That single fact, no free-electron sea, is why most ceramics do not conduct electricity or heat well and are neither shiny nor ductile. Compare table salt NaCl (inorganic and nonmetallic, but water-soluble and never fired, a borderline case) with alumina Al2O3, the textbook ceramic.

The definition has fuzzy edges, and that is honest science rather than sloppiness. Graphite and diamond are pure carbon (an element, here treated as inorganic) and are often grouped with ceramics for their hardness and refractoriness. Some ceramics do conduct: yttria-stabilized zirconia (YSZ) carries oxygen ions, and cuprates superconduct. So 'nonmetallic' describes the bonding and origin, not a guarantee of zero conductivity.