The emergence of new intelligent applications has fostered the development of a task-oriented communication paradigm, where a comprehensive, universal, and practical metric is crucial for unleashing the potential of this paradigm. To this end, we introduce an innovative metric, the Task-oriented Age of Information (TAoI), to measure whether the content of information is relevant to the system task, thereby assisting the system in efficiently completing designated tasks. We apply TAoI to a wireless monitoring system tasked with identifying targets and transmitting their images for subsequent analysis. To minimize TAoI and determine the optimal transmission policy, we formulate the dynamic transmission problem as a Semi-Markov Decision Process (SMDP) and transform it into an equivalent Markov Decision Process (MDP). Our analysis demonstrates that the optimal policy is threshold-based with respect to TAoI. Building on this, we propose a low-complexity relative value iteration algorithm tailored to this threshold structure to derive the optimal transmission policy. Additionally, we introduce a simpler single-threshold policy, which, despite a slight performance degradation, offers faster convergence. Comprehensive experiments and simulations validate the superior performance of our optimal transmission policy compared to two established baseline approaches.