Blockchains are generally classified as one of 3 general archetypes; public, private & consortium. A public Blockchain is a permissionless system that adopts an open governance apporach.
Public Blockchains are permissionless, meaning that they allow for easy joining and leaving of the network consensus, there is no authoritative figure controlling who can and cannot participate. In a Public Blockchain environment economic incentives keep actors from acting maliciously and keep them interested enough to continue participation. Due to the governance structure of Public blockchains, the most common consensus mechanism utilized is Proof-of-Work, however newer generation projects have modified PoS consensus algorithms to enable permissionless participation.
Some examples of public blockchain projects are Bitcoin, Ravencoin, Horizen & Ethereum.