The Tangle is the data structure at the heart of IOTA, first introduced in the IOTA white paper. This section will give a short introduction to what the tangle is and how it works. For a more in-depth treatise, please check out the white paper or this blog series.
IOTA uses a DAG instead of a blockchain to store its ledger. The main motivation is scalability: a blockchain has an inherent transaction rate limit, due to the conflict between block sizes and block issuances rates. If blocks are issued too frequently, or are too large, forks will occur often. When a fork happens, several new blocks are added to the chain at similar times, and the network must somehow decide between them.
In a DAG, we accept that forks can and will occur often; however, unlike in a blockchain, a fork is not final. Diverging branches can be merged back together, as long as they are consistent with each other. The transaction rate is therefore bounded only by the latency between the nodes.
A DAG may be thought of as an alternative to a blockchain, which favors Availability over Consistency.
The Tangle is a DAG, where vertices represent transactions, and edges represent approvals:
If there is an edge from A to B, we say that "A approves B". When a node issues a new transaction, it must choose 2 previous ones to approve, thereby adding 2 new edges to the graph.
If there is some directed path from A to B, we say that that A references B.
The first transaction in the Tangle is referred to as the genesis. All the IOTA tokens were created in the genesis, and no new ones will ever be created. All transactions in the tangle reference the genesis directly or indirectly.
Transactions with no approvers are called tips. Nodes are expected to choose tips to approve, rather than older transactions, because this helps move the network consensus forwards. The method for choosing which two tips one should approve is one of the key innovations of IOTA, and will be introduced in the Tip selection section.
Each transaction contains payment information, in the form of "A paid B X IOTAs". Approving a transaction implies verifying that it does not break the consensus rules: in particular, that none of the accounts have negative balances. It also implies that the two chosen transactions do not contradict each other.