Uses of a silicon semiconductor and why its resistance at different temperatures
It's the energy-band model. The idea is materials have separated conduction and valence bands in which electrons may reside. 

Eg is the size of the gap between these bands. In metals, the gap is zero, the bands overlap. In insulators, the gap is so huge that it is impossible for electrons to reach the valence band (temperature >>1000K needed). Semiconductors are inbetween, the gap is a few eV (Si: 1eV@300K).

In think this "intrinsic region" should just mean "temperature-depending conduction" in contrast to the conduction introduced by doping atoms. The latter change the energy niveaus of the bands and the size of the band gap. When the temperature is sufficiently low, there are other effects which govern the resistance measured instead (meaning: it's still there but you cannot measure it independently.)