Isolated atoms have distinct energy levels, very much like the electron energy level of hydrogen that you draw in the energy level topic.
Using a graph of energy level vs atomic separation , these distinct line spread into two lines (like the tongue of a snake) . Between these two lines is a region where the electron can exist , hence energy band. You may call the upper band (which is unfilled in semiconductor) conduction band. The lower band (filled in semiconductor) is known as valence band.
If you select a particular atomic separation by drawing a vertical line , you will notice the separation of the two bands are different depending where your vertical line is . The separation between these bands could be very close as in the case of semiconductor and very far in the case of insulator.
Take carbon , the separation is so large 5.5 eV that makes it qualify as an insulator .For silicon at a larger atomic separation the energy separation of the two band is 1.1 eV which makes it a semiconductor.