Most written natural languages are composed of sequences of words and sentences. Similar to humans, large language models (LLMs) exhibit flexibility in handling textual positions - a phenomenon we term position generalization. They can understand texts with position perturbations and generalize to longer texts than those encountered during training with the latest techniques. These phenomena suggest that LLMs handle positions tolerantly, but how LLMs computationally process positional relevance remains largely unexplored. This work connects the linguistic phenomenon with LLMs' computational mechanisms. We show how LLMs enforce certain computational mechanisms for the aforementioned tolerance in position perturbations. Despite the complex design of the self-attention mechanism, this work reveals that LLMs learn a counterintuitive disentanglement of attention logits. Their values show a 0.959 linear correlation with an approximation of the arithmetic sum of positional relevance and semantic importance. Furthermore, we identify a prevalent pattern in intermediate features, which we prove theoretically enables this effect. The pattern, which is different from how randomly initialized parameters would behave, suggests that it is a learned behavior rather than a natural result of the model architecture. Based on these findings, we provide computational explanations and criteria for LLMs' position flexibilities. This work takes a pioneering step in linking position generalization with modern LLMs' internal mechanisms.