Metals conduct electricity well due to the fact that the outermost electrons in their atoms are held by weak atomic forces, allowing these electrons to flow easily from one atom to another. This flow of electrons is what lies at the heart of an electric current.
The type of bonds that atoms create with one another depends on their atomic configuration. Each atom has a varying number of electrons, arranged in shells representing increasing energy states. If a shell has the maximum number of electrons it can hold, it is relatively stable, while a shell with fewer electrons can more readily give and take electrons. Organic molecules tend to feature bonds that fill out these electron shells, while metals tend to have more gaps in the outermost shell. In strong conductors, such as copper, free electrons flow around the metallic atoms like water around islands, moving freely from one atom to the next.
When an electric field is applied to a metal, it causes these electrons to move from place to place. Since each electron shares the same electrical charge, the particles repel one another strongly. One free electron shifts to the adjacent metal atom, dislodging any free electrons present, causing them to move in the direction of the current.