Matthew Beedham describes a permissionless blockchain as one where the public validates transaction information on the network.
In permissioned systems, transaction information is validated by a select group approved by the blockchain’s owner, hence a private blockchain.
Permissioned systems tend to be more scalable and faster, but are more centralized. Permissionless systems are open for all to join, and as a result, usually more decentralized, the trade off is speed and scalability.