Going beyond mimicking limited human experiences, recent studies show initial evidence that, like humans, large language models (LLMs) are capable of improving their abilities purely by self-correction, i.e., correcting previous responses through self-examination, as seen in models like OpenAI o1. Nevertheless, little is known about how such capabilities arise. In this work, based on a simplified setup akin to an alignment task, we theoretically analyze self-correction from an in-context learning perspective, showing that when LLMs give relatively accurate self-examinations as rewards, they are capable of refining responses in an in-context way. Notably, going beyond previous theories on over-simplified linear transformers, our theoretical construction underpins the roles of several key designs of realistic transformers for self-correction: softmax attention, multi-head attention, and the MLP block. We validate these findings extensively on synthetic datasets. Inspired by these findings, we propose a simple self-correction strategy, Checking as Context (CaC), which finds novel applications in alleviating social bias and defending against LLM jailbreaks. We believe that these findings will inspire further research on understanding, exploiting, and enhancing self-correction for building better foundation models. Code is at https://github.com/yifeiwang77/Self-Correction.