Narrowing in itself is a simple operation. Narrowing computations are executed step-wise until the term subject of a computation can no longer be narrowed. In general, many narrowing steps are possible in a term. Determining which steps are useful for a computation is the task of a strategy. Different strategies have been proposed for different classes of rewrite systems.
Good strategies are sound, complete and efficient.
These concepts are best understood when the term subject of a narrowing computation is an equation. Soundness means that narrowing computes only solutions of the equation. Completeness means that narrowing computes all the solutions of the equation. Efficiency is more elusive. A narrowing strategy computes a set of narrowing steps of a term.