The Hashgraph is a novel solution to a well known computer science problem known as the Byzantine Generals problem. Byzantine Generals refers to a class of problems that arise in distributed computing where multiple independent computers (known as "nodes") need to coordinate and all come to consensus on some question. Solutions to this problem are known as Byzantine Fault Tolerant (BFT). The most secure solutions are known as Asynchronous Byzantine Fault Tolerant (ABFT). A less secure subset are known as Practical Byzantine Fault Tolerant (PBFT) and are known as "practical" because, before Hashgraph, there we no known high performance ABFT implementations. Thus, "practical" solutions were devised that, while less secure, worked well in a controlled, centralized environment.
The Hashgraph algorithm complete changed the game. It is now possible to implement the most secure networks using ABFT consensus with incredible performance characteristics. The Hashgraph made ABFT practical for an incredibly wide range of applications.
Distributed consensus is the heart of the problem that must be solved by all blockchains. A leaderless, ABFT consensus algorithm fundamentally solves numerous problems with Proof-of-Work and other consensus algorithms. It is fast, fair, secure, and mathematically proven to reach consensus with 2/3 of all nodes being honest in the network.
A full ledger requires some of each type of node. A ledger must have validators to process transactions. It must have block nodes so the blockchain data can be saved. It must have historian nodes for querying historical information on the chain. In addition, a ledger may have an Ethereum RPC Relay, which is a node that implements the Ethereum JSON-RPC APIs, essentially allowing the Hashgraph ledger to look like an Ethereum node to standard Ethereum applications and wallets, like MetaMask.
A network of validators, which each accept transactions, run the Hashgraph algorithm to determine their fair order and timestamp, and which execute those transactions to modify the current ledger state. Validator nodes form the basis of trust in the network. Validators each produce an identical blockchain.
Validators upload their blockchain to block nodes. A block node keeps a complete copy of the blockchain. They have an API for querying the full chain, or a subset of the chain, and for querying snapshots of the ledger state.
Historians read the blockchain from a block node and create indexes over the data in the blockchain. They provide REST, GraphQL, or other APIs that application programmers can use to query the blockchain state. Historians may store all historical data, or they may store only a subset of the data.