Directed Acyclic Graph (DAG) is a distributed ledger system that serves as an alternative to blockchain systems. Blockchains use a single, linear chain of blocks with each block referencing its predecessor. When the the blockchain splits into two, a temporary fork is created and the shorter branch of the chain is orphaned (and the work done on this abandoned chain goes to waste). In contrast, DAGs allow these branches to coexist, and thus for multiple, interconnected chains to exist. That is, blocks can exist parallel to each other as long as the chains continue to move in the same direction (only referencing preceding or parallel blocks).
By accepting orphan blocks, DAGs are able to maintain a higher rate of transactions per second than blockchains. Further, allowing multiple chains to coexist eliminates the effort that would be wasted by abandoning all but one. However, DAGs are considered by some to be less secure than blockchains. IOTA is currently the most notable project utilizing this technology and refers to its DAG system as ‘Tangle.’