metallic bond
Why is a block of copper shiny, easy to bend, and a good conductor, while salt is dull and brittle? The difference is the metallic bond. In a metal, the atoms are packed close together and each one lets its outer electrons wander freely through the whole piece, like a fluid. The fixed positive ion cores sit in a sea of these mobile electrons, and the attraction between the cores and the electron sea holds the metal together.
The simplest picture is the electron-sea model: the metal is a regular array of cations bathed in delocalised valence electrons that belong to no single atom. Because the electrons are not tied to any one bond, the ion cores can slide past one another without breaking the bonding (so metals are malleable and ductile), the electrons can drift under a voltage (so metals conduct electricity), and they can carry energy quickly (so metals conduct heat). A fuller treatment replaces the sea with energy bands, but the intuition is the same: bonding electrons are shared across the whole solid, not localised between two atoms.
Metallic bonding is the third limiting bond type alongside ionic and covalent, and it dominates the chemistry and physics of most of the periodic table. Its strength varies enormously — mercury is liquid at room temperature while tungsten melts above 3400 degrees Celsius — depending on how many valence electrons each atom contributes and how tightly the cores hold them. The same delocalised electrons that conduct also reflect light, which is why polished metals are lustrous.
Hammer a copper rod and it flattens instead of shattering: the Cu+ cores simply slide to new positions while the electron sea flows around them and keeps bonding. Compare an ionic crystal, where sliding brings like charges together and the crystal cracks.
Malleability falls straight out of the electron-sea picture.
The electron-sea model is only a first sketch; it cannot explain why some elements are insulators or semiconductors. Band theory of solids is the honest, fuller account of why metals conduct and non-metals do not.