A good technical overview:
Delegated Proof of Stake uses a reputation system and real-time voting to achieve consensus. To be more specific, a panel of trusted parties has to be established, with all of its members eligible to create blocks and prevent non-trusted parties from participating. Delegates, the parties responsible for creating blocks, are unable to change transaction details. However, they can prevent specific transactions from being included in the next network block. This seemingly requires a fair bit of trust, which makes the concept look far less appealing.
Using Ark as an example:
All account holders of Ark can vote 51 delegates. These 51 delegates are allowed to do updates to the database. As each Ark counts as vote the delegates represent all stakeholders of the Ark network.