The nonclassical properties of quantum states are of tremendous interest due to their potential applications in future technologies. It has recently been realized that the concept of a resource theory is a powerful approach to quantifying and understanding nonclassicality. To realize the potential of this approach, one must first find resource theoretic measures of nonclassicality that are operational, meaning that they also quantify the ability of quantum states to provide enhanced performance for specific tasks, such as precision sensing. Here we achieve a significant milestone in this endeavor by presenting such an operational resource theoretic measure. In addition to satisfying the requirements of a resource measure, it has the closest possible relationship to the quantum enhancement provided by a nonclassical state for measuring phase-space displacement: It is equal to this enhancement for pure states and has a tight upper bound on it for mixed states. We also show that a lower bound on this measure can be obtained experimentally using a simple Mach-Zehnder interferometer.