Tangle
The Tangle is a directed acyclic graph (often referred to as DAG). The Tangle is made up of multiple individual nodes, and operates as a type of distributed ledger. This allows for the storing of transactional information and transfer of funds. The Tangle is notably related to the IOTA project, and its quest for a free and decentralized payment system.
In ordinary layman terms the Tangle differs from Bitcoin (and other blockchain based currencies) in the following way: The blockchain can only process one transaction at a time, which has led to congestion as more users begin to utilize the network. Each transaction is then verified by multiple parties (called miners), before it is added to the central ledger. On the other hand, the Tangle carries no economic incentive. Instead, it is designed in a way that requires all users to verify two transactions each time they wish to carry out one of their own. As more users begin to utilize the Tangle, the collective hashing power will increase and provide for faster transactions.
Here is an illustration of the Tangle, as it is visualized by an artist:
