In recent years, semantic communication is progressively emerging as an effective means of facilitating intelligent and context-aware communication. However, current researches seldom simultaneously consider the reliability and timeliness of semantic communication, where scheduling and resource allocation (SRA) plays a crucial role. In contrast, conventional age-based approaches cannot seamlessly extend to semantic communication due to their oversight of semantic importance. To bridge this gap, we introduce a novel metric: Age of Semantic Importance (AoSI), which adaptly captures both the freshness of information and its semantic importance. Utilizing AoSI, we formulate an average AoSI minimization problem by optimizing multi-source SRA. To address this problem, we proposed a AoSI-aware joint SRA algorithm based on Deep Q-Network (DQN). Simulation results validate the effectiveness of our proposed method, demonstrating its ability to facilitate timely and reliable semantic communication.