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A narrow line region (NLR or narrow emission-line region) is whatever region produces narrower emission lines at an active galactic nucleus (AGN), in contrast to the broad line region (BLR), which is whatever region produces the broader lines. "Narrow" is relative: the narrow lines have considerable line broadening, but significantly less than the broader lines. The broadening in both cases is Doppler broadening, a sign of the temperature of the gas.
The attractive current theory (termed the unified model) is that a substantial torus-shaped cloud with considerable dust surrounds the supermassive black hole (SMBH) and its accretion disk. Material in that inner, partially-hidden region has a high velocity and temperature, leading to the broad lines. Material further from the SMBH is somewhat heated by the accretion emission, forming the narrower lines that are not blocked from our view by the torus. This explains the fact that observed AGNs generally show the narrow lines but only some show the broader lines, the latter which we see when our viewing angle is such that we see what is encircled by the torus.