Plato's Republic is quite possibly, the most philosophically significant work of Ancient Greece. Its Cave allegory put that we do not know about it, even if something exists in reality, we will be in disbelief about it. In one word, the allegory is about truth. The actual allegory is much more story-like; I encourage you to read it. Please do, this blog post will be about its relevance.
So, does it ring familiarity with you? With no doubt, The Matrix came to mind. The Allegory of the Cave plays a major part in The Matrix. Especially in the "steak scene" where the character Cypher, strikes a deal with Agent Smith, to return him to the Matrix and wipe him of memories of the "real world". "Ignorance is bliss", he remarks, understanding that the truth is indeed painful. Now, Cypher's reaction is natural. It can be seen in real-life. Imagine that the country is currently in a prosperous, secure yet free state. Then you discover that the NSA has been wiretapping your phone calls, intercepting your emails and blocking out your blog posts. Infuriated by this, would you not want to have never known about such evils?
So, what is a more relevant connection to our life? That is history. It is the job of the historian to supply people with the truth. Even primary historical documents give shaky grounds for proving that things really did happen. As fun as prehistory is, we will never truly be sure if what we know is the truth, as we can only be truly sure of something's existence by first handedly witnessing it happen. The historian must tell the truth in order to prevent cave-like, or NSA situations from happening in the future. As it is said, we study history to prevent the future from repeating the mistakes of the past. Similarly, history is not the dry study of what dead guys did, but supplying the truth to the unborn guys to prevent them from doing what the dead guys did wrong.