What is the longest chain rule Nakamoto Consensus?

Could you please elaborate on the concept of the longest chain rule in the Nakamoto Consensus? I'm particularly interested in understanding how it functions within the framework of cryptocurrency and blockchain technology. Specifically, how does the longest chain rule determine the validity of transactions and ensure the security of the network? Is it related to the concept of mining and the proof-of-work algorithm? Additionally, how does it help in resolving conflicts or forks that may arise in the blockchain?