Question: How are weights dynamically adjusted?
Answer: One can think $(1-p_{i1})$ as a weight associated with each example, which changes as training proceeds. The intuition of changing $p_{i1}$ to $(1-p_{i1}) p_{i1}$ is to push down the weight of easy examples. For easy examples whose probability are approaching 0 or 1, $(1-p_{i1}) p_{i1}$ makes the model attach significantly less focus to them. Figure FIGREF23 gives gives an explanation from the perspective in derivative: the derivative of $\frac{(1-p)p}{1+(1-p)p}$ with respect to $p$ approaches 0 immediately after $p$ approaches 0, which means the model attends less to examples once they are correctly classified.
Alternative answer: associates each training example with a weight in proportion to $(1-p)$, and this weight dynamically changes as training proceeds