The resonance frequency of plasmonic nanoparticles can be altered by a minute change of their local refractive index, making them a great tool for bio-sensing. In this work, we investigate the sensitivity of plasmonic naonsensors in theory. By treating plasmonic nanoparticles as nanocavities, we solve the eigenmodes (i.e., the plasmonic resonance modes) of the system, calculate the analyte-induced resonance frequency shifts using the perturbation theory, and obtain explicit formulas for the spectral sensitivity of plasmonic naonsensors in three major different types of sensing experiments, namely, single molecule detection, thin absorption layer sensing, and index sensing of bulk solutions. In the single molecule case, a linear relation is found between the spectral sensitivity and the local intensity of electric fields. When analytes form a thin layer on a plasmonic nanosensor, the induced resonance shift is proportional to the integral of the intensity of local fields over the covered area. When the analytes are homogenously distributed in the surrounding medium, the index-change-induced spectral change is, however, only decided by the material property of the nanocavity independent with the local fields. We compared the theory with both numerical results and previously reported experimental results, and good agreements are found. This work provides explicit guidelines for designing high-performance sensing system for a broad range of applications.