How do themes in literature help us to understand ourselves?
This is a very interesting question, and one with many implications. One answer that occurs to me, based upon something a writing teacher of mine (John Edgar Wideman, whose works are discussed elsewhere on this website) said in graduate school, which was that reading fiction teaches empathy. The full context of his remark was that he felt our society was becoming less hospitable and less charitable because people were reading much less fiction, and it was reading fiction that allowed people to imagine themselves in the situations of other people, to put themselves in someone else's shoes, so to speak. The idea that reading fiction teaches empathy allows us to understand how themes in literature can impact our own lives, at the very least helping to clarify our perspective and maybe even shift it.
When fictional characters experience extraordinary circumstances, readers may respond with a variety of emotions depending upon those circumstances (excitement, pity, anger, curiosity, etc.) Even when these stories include events we can barely imagine happening to us, the people experiencing them are usually like us in many ways. This is how literary themes can create a bond and a bridge for readers to relate to stories. Themes involving common human emotions (jealousy, regret, grief, etc.) can help us to explore our own experiences, and show us examples of how characters react to the events that take place in stories. Of course, great literature does not always portray ideal human behavior: sometimes we learn lessons on how not to act.
Wider themes that refer to the social condition (such as the tyranny of poverty, or the idea that compassion triumphs over evil) can help us to understand more complex ideas and apply them to historical or current events, but also to our own situations. Many readers have their own personal literary heroes who inspire them with admirable behavior, and we try to uphold their best qualities as models for living: Jane Eyre's resilience, for example, or Jay Gatsby's determination, or Tom Sawyer's cleverness, or Elizabeth Bennet's honesty.