Instagram's disappearing-message feature in Direct is called Vanish mode.
Vanish mode lets participants exchange messages, photos, videos, and other content that disappears after it has been seen and the chat is left. It is designed for temporary conversations rather than permanent message history, and users can typically enter the mode by swiping up within a Direct conversation.
The feature belongs to Instagram Direct, Instagram's private-messaging system, which launched in December 2013. Direct originally focused on sending private photos and videos; ephemeral messaging arrived earlier, in 2016, before Instagram later introduced the more unified Vanish mode experience.
Vanish mode is often confused with unsending a message. Unsending removes a particular message, while Vanish mode changes the conversation into a temporary mode. It is also distinct from ordinary disappearing photos or videos sent through Direct, which are temporary media rather than an entire chat mode.