Timely status updating is crucial for future applications that involve remote monitoring and control, such as autonomous driving and Industrial Internet of Things (IIoT). Age of Information (AoI) has been proposed to measure the freshness of status updates. However, it is incapable of capturing critical systematic context information that indicates the time-varying importance of status information, and the dynamic evolution of status. In this paper, we propose a context-based metric, namely the Urgency of Information (UoI), to evaluate the timeliness of status updates. Compared to AoI, the new metric incorporates both time-varying context information and dynamic status evolution, which enables the analysis on context-based adaptive status update schemes, as well as more effective remote monitoring and control. The minimization of average UoI for a status update terminal with an updating frequency constraint is investigated, and an update-index-based adaptive scheme is proposed. Simulation results show that the proposed scheme achieves a near-optimal performance with a low computational complexity.