DAO stands for Decentralized Autonomous Organization. It is a concept that arises from self enforcing smart contracts.
If an organization is able to encode all of its business operations, business rules and workflows in a smart contract, then this organization can function in a completely decentralized way, with the smart contract enforcing the rules, paying the collaborators' wages and obligations with partners and so on.
As you can imagine, this kind of smart contract, if fully implemented, would become absurdly complex. This has led to problems in the first few attempts at implementing a DAO via Ethereum smart contracts. For instance, "The DAO" project which received over U$ 150 million funding attempted to implement one such autonomous organization, only to have a serious flaw discovered in its smart contract. The flaw allowed attackers to steal one third of all the funds raised. This hack led to an Ethereum hard fork which meant to recover the large stolen sums. The decision to save The DAO's resources via a hard fork was not unanimously accepted, leading to the creation of Ethereum Classic which kept the original Ethereum blockchain where the funds were stolen.
Since The DAO heist, there have been great improvements in smart contract development practices, especially concerning security.
DAO's are a very interesting concept, which could shape future work relations and allow fully distributed teams to work around the world while getting paid in cryptocurrency. With the advances in smart contract development we should see more and more DAO's being implemented, most likely in modules which can be more easily debugged.