Nakamoto consensus is consensus as it is defined in the Bitcoin whitepaper where nodes vote to enforce the rules used to build the blocks that make up the Bitcoin public ledger.
Nakamoto Consensus defines an honest node as a node that seeks out the longest valid chain of blocks and applies proof of work to extend that chain. In this context, the longest chain represents greatest proof-of-work effort on the valid chain. If the majority of nodes are honest, then the honest chain will grow with the greatest proof of work and outrun any other competing chains.
By choosing which chain to build upon, the nodes vote to enforce the rules that govern the protocol and use of the Block chain as a global financial ledger with legal and regulatory oversight.
Through Nakamoto consensus, proof of work on the longest chain becomes an economic and technical barrier for any attacker to overcome. At the same time, the block reward as an economic incentive drives the node to follow the consensus encouraging honesty and cooperation between competing enterprise miners.
The security of Nakamoto consensus has been studied by academia and tested in the real world since 2009.