in addition to the above mentioned links, just in brief, keep in your mind that band structure presents the allowed energy, i.e. eigenvalue of the Schrodinger equation. So, if you know until which energy, orbitals are occupied, you can first of all determine the Fermi energy of the system. if at this level there was no gap in band structure, you are studying a metal, otherwise when there is a band gap, you are studying an insulator or a semiconductor regarding the bigness of the band gap.
In an isolated atom, bound electrons have discrete energy levels. In solids, which are composed of many atoms which are closely packed, allowed discrete energy levels no longer remain discrete. Due to perturbative effects caused by electrons/nuclei of other nearby atoms, discrete energy levels transform into allowed energy bands. It is possible that two such allowed bands overlap each other, but it is also possible otherwise; that is the two bands are disjoint. In case of two allowed bands being disjoint, the energy gap which is seen between two allowed bands is called the band gap.
Lowest possible energy band is the valence band where electrons are bound to respective atoms, which may be partially or completely filled. Next available energy band is the conduction band, which may be partially filled or empty. If there is no energy gap between conduction and valence band, then the solid is a conductor, but if there exists a gap then the solid is either an insulator or a semiconductor, depending of the size of the gap. If case of insulators it is a wide gap whereas in case of semiconductors the gap is narrow.