A DAO is a decentralised organisation where the (anonymous) participants have a say on a list of proposals depending on the amount they have staked in the organisation. This enables decentralised applications of centralised systems like voting and community participation to happen with anonymity and privacy.
A DAO can be used by entities to vote on project timelines, to vote on whether they are satisfied with the project's deployment, to vote on what projects to include on the platform and more. It could also be used when deciding on timelines for platform development, who's responsible for developing the platform, features to be added to the platform, etc.
This model would have to be supplemented by a base layer blockchain which handles the non governance part of the infrastructure. The base layer should be Ethereum-L1 since only then can people vote or stake on proposals with ETH. Having a different base layer blockchain would mean that people deal with three types of currencies - a stablecoin to invest in projects, ETH to take part in the DAO and the base layer blockchain's native coin.
The trust model is that one trusts the algorithm the DAO is based on to take actions based on the majority of votes cast for or against a proposal.