In communications, narrowband is defined as a lower rate of transmission in contrast to a higher "wideband" rate. The metrics are different depending on the type of communications, and the narrowband upper limit changes as time and technology move forward.
For example, a radio channel of 25 kHz or less has been considered narrowband, and everything above to be wideband. In digital transmission, the upper limit of narrowband was 150 bps (bits per second) decades ago. The narrowband threshold has already increased to 2,400 bps, 64 Kbps and 1.544 Mbps (T1 speed). Contrast with wideband