Hedera Hashgraph explained

Hashgraph is an alternative to blockchain — the first-generation tech with severe constraints in terms of speed fairness cost security. A fundamental bottleneck has been the performance — how many applications are there that can run on a database that can do 5 transactions per second? — Harmon CEO of Hashgraph
Its data structure and associated distributed consensus algorithm that uses 2 techniques to reach consensus “Gossip about Gossip” and “Virtaul Voting”
Developed by Leemon Bair Ph.D. in mid-2016 and is the intellectual property of this company Swirlds.
It's considered fast because of its use of the “gossip about gossip” protocol, which spreads messages across the network fast and it works in a private, permission-based setting.

In a non-permission setting (aka public blockchain) like in Bitcoin, the nodes participating in the consensus protocol are not known beforehand and untrusted since a node is allowed to join the network at will. Proof of Work solves this.
In private( permissioned ) distributed ledgers, identities of all nodes are known beforehand and the network is not open to an arbitrary participant. The prior knowledge of the participating nodes provides natural protection against Sybil attacks and makes it easier to reach consensus. No need for proof of work.
Thus, its throughput should not be compared with public blockchains like Bitcoin or Ethereum (10 transactions per second) as it is equivalent to compared apples with oranges.
If one transaction reaches two-thirds of the network ahead of other transactions, it is considered to be the first.
Hashgraph is an asynchronous Byzantine Fault Tolerant and it is not deterministic.
Byzantine Fault Tolerance is property o a system — system is said to be Byzantine Fault Tolerant if it can continue to operate even if certain participants drop out or are adversarial.
For deterministic protocols, all honest nodes reach consensus by round r for some a priori knew constant r. For non-deterministic or probabilistic protocols, the probability that an honest node is undecided after r rounds approaches zero as r approaches infinity

If and when used in a public setting. Hashgraph will face the same issues that other public blockchains are facing today and may not be able to maintain its security and performance.
Scalability is still an open problem for public blockchains. Ethereum uses PoS for its Casper protocol, NEO employs dBFT, EOS has a dPOS-based solution, and Zilliqa implements sharding. All these solutions have their own benefits and weakness as there is no silver bullet to solve the scalability problem
What is scalability? The number of users? The number of transactions? Size of the network?

Hashgraph currently scales only in the number of transactions processed but does not scale with the number of nodes in the network.
In the blockchain, data is stored in blocks that contains all the transactions made in a given period of time, a timestamp, the hash of the block and the hash of the previous block.
In the hashgraph, data is stored in events that contains a timestamp and transaction just like a block and two regular hashes.

White paper — https://www.hedera.com/hh-whitepaper-v2.0-17Sep19.pdf
API docs — https://docs.hedera.com/docs/hedera-sdks
Twitter — https://twitter.com/hashgraph
Telegram — https://t.me/hederahashgraph
Website- https://www.hedera.com/