The term ‘narrow-wide’ refers to the width of the chainring teeth, which are made alternately narrow and, er, wider. It’s designed to retain the chain on a single-chainring bike without recourse to a chain guide mounted at the bottom bracket or seat-tube.
The idea is that the wider teeth fit between the chain’s outer plates and the narrower teeth between the more closely-spaced inner ones in order to lessen or obviate the likelihood of chain derailment when the chain is flapping around on bumpy terrain. Many users affirm that this is indeed the case, indicating that the concept has practical merit. The chainring must, of course, have an even number of teeth.
Cycle's Technical Editor