Why do some materials conduct electricity and others do not?
Because of whether a material has electrons free to move, which in turn depends on how its atoms share them — and the answer is genuinely quantum-mechanical rather than a matter of how tightly electrons are held.
The simple version. In a metal, atoms give up their outer electrons into a shared pool that belongs to the whole lattice rather than to any atom. Apply a voltage and that pool drifts. In an insulator, electrons are locked into bonds between specific atoms and there is nowhere for them to go.
The real version: energy bands. When atoms are brought together, their electron energy levels spread into continuous bands separated by gaps in which no electron can exist. What matters is the band gap between the highest filled band and the next empty one.
Conductors have a partly filled band, so electrons have adjacent empty states to move into at essentially no energy cost.
Insulators have a full band and a large gap — several electron volts — so no ordinary voltage can lift an electron across.
Semiconductors have a full band and a small gap, around one electron volt. At absolute zero they insulate; at room temperature thermal energy pushes some electrons across, and conductivity can be controlled by heat, light or added impurities. That controllability is the whole basis of electronics.
What follows from this picture:
Doping. Adding tiny quantities of another element introduces spare electrons or spare holes, converting silicon into a controllable conductor — the foundation of transistors.
Temperature behaves oppositely. Metals conduct worse when heated, because lattice vibrations scatter the drifting electrons. Semiconductors conduct better, because heat frees more carriers. This difference is diagnostic.
Superconductivity, below a critical temperature in some materials, where electrons pair up and resistance vanishes entirely — not merely becomes small.
Water is a poor conductor when pure; it is the dissolved ions that conduct, which is why distilled water is far less dangerous than tap water and why salt water is worse still.