Unlike the Urysohn's metrization theorem which provides a sufficient condition for metrization, this theorem provides both a necessary and sufficient condition for a topological space to be metrizable.
The theorem was proven by Bing in 1951 and was an independent discovery with the Nagata-Smirnov metrisation theorem that was proved independently by both Nagata (1950) and Smirnov (1951). Both theorems are often merged in the Bing-Nagata-Smirnov metrisation theorem. It is a common tool to prove other metrisation theorems, e.g. the Moore metrisation theorem: a collectionwise normal, Moore space is metrisable, is a direct consequence.