Delay in the Integral is a smart contract that serves as an intermediary layer between users and the Integral pool contracts. All user interactions with the Integral (swap/deposit/withdraw, etc) will be done through the delay contract. In particular, every user action (swap/deposit/withdraw) will experience a delay.
The key parameter (governance controlled) in the delay contract is the delay parameter. It dictates the time period that has to elapse before any particular user action can start to be processed. The delay parameter can range from minutes to a week. This delay parameter is also the time duration of the TWAP window.
Due to the delay mechanism, only the delay contract can directly interact with the pair contract, i.e. all the swap/deposit/withdraw actions have to be invoked by the delay contract, and cannot be triggered by anyone else.