Why metal is ductile and malleable?

As metal atoms are packed in layers in giant metallic structure, layers of metal atoms can slip over one another after sufficiently strong external force is applied.
As a result, the shape of metal is change without breaking the metallic.

Why metal is malleable?
Metal is malleable because its delocalized valence electrons; metallic bonds occur among metal atoms. A sea of valence electrons surrounds positive metal ions. The electrons are free to move throughout the resulting crystal. The delocalized nature of the electrons explains a number of unique characteristics of metals: they are good conductors of electricity, they are ductile (meaning they can be made into wires) and they are malleable, (they can easily be hammered into thin sheets).
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Why metal is ductile?
Because atoms of metal lose their outer electrons which then become delocalized, and free to move throughout the entire metal. These -ve delocalized electrons hold the metal cations together strongly. Since these electrons can flow, atoms with metallic bonding exhibit high electrical conductivity. The number of valence electrons involved in the bonding and the strength of the nucleus charge determines the strength. Unlike ionic bonding, distorting the atoms does not cause repulsion so metallic substances are ductile (can be stretched into wires) and malleable (can be made into flat sheets). The free moving electrons also allow for high thermal conductivity, and the electrons can carry the heat energy rather than it being transferred slowly through atoms vibrating.