In the absence of extensive human-annotated data for complex reasoning tasks, self-improvement -- where models are trained on their own outputs -- has emerged as a primary method for enhancing performance. Recently, the approach to self-improvement has shifted toward a more dynamic, online fashion through iterative training processes. However, the critical factors underlying the mechanism of these self-improving methods remain poorly understood, such as under what conditions self-improvement is effective, and what are the bottlenecks in the current iterations.In this work, we identify and propose methods to monitor two pivotal factors in this iterative process: (1) the model's ability to explore and generate high-quality responses among multiple candidates (exploration); and (2) the reliability of external rewards in selecting the best responses from the generated outputs (exploitation).These factors are inherently moving targets throughout the self-improvement cycles, yet their dynamics are rarely discussed in prior research -- It remains unclear what impedes continual model enhancement after only a few iterations. Using mathematical reasoning as a case study, we begin with a quantitative analysis to track the dynamics of exploration and exploitation, discovering that a model's exploratory capabilities rapidly deteriorate over iterations, and the effectiveness of exploiting external rewards diminishes as well due to shifts in distribution from the original policy.Motivated by these findings, we introduce B-STaR, a Self-Taught Reasoning framework that autonomously adjusts configurations across iterations to Balance exploration and exploitation, thereby optimizing the self-teaching effectiveness based on the current policy model and available rewards.Our experiments in mathematical reasoning demonstrate that B-STaR not only enhances the model's exploratory capabilities throughout training but also achieves a more effective balance between exploration and exploitation, leading to superior performance. Crucially, this work deconstructs the opaque nature of self-training algorithms, elucidating the interpretable dynamics throughout the process and highlighting current limitations for future research to address.