A hashgraph is a patented data structure developed by Hedera Hashgraph Founder and Chief Scientist Professor Leemon Baird . A hashgraph stores and updates information in accordance with a unique algorithm that allows a distributed and decentralised community to reach consensus between nodes/members in a fast (250,000 transactions per second) and secure (Strong Form Byzantine Fault Tolerant) way with mathematically proven fairness in the absolute ordering of transactions.
The data structure is organised using Directed acyclic graph (DAGs), where each vertex contains the hash of its two parent vertices. A hashgraph is updated by gossip where each member repeatedly chooses another member at random who gives them all the events that they don't yet know.
A hashgraph utilizes an entirely new protocol called "gossip about gossip" for information sharing. This means that part of the information transferred between members is an abbreviated history of how members have spoken to other members. This is similar to how friends may "gossip about what Bob did."
The information stored in a hashgraph is a history of how everyone gossiped. When Alice tells Bob everything she knows during a gossip sync, Bob creates a new block or "event" which commemorates the occurrence. The event becomes a vertex in the graph containing Bob's most recent event, the hash of Alice's most recent event, a timestamp, along with any new transactions that Bob wants to create at that moment. Combined, the hashgraph is the set of all known events. A hashgraph was first proposed in a white paper by Baird titled " The Swirlds Hashgraph Consensus Algorithm: Fair, Fast, Byzantine Fault Tolerance "  .
Baird conducted an interview with Hidden Forces, Episode #22 "The Future of Distributed Ledger Technology is not Blockchain, It's Hashgraph  ."