Definition
Chat and phone apps process incoming content before the user opens it. They build a preview, a thumbnail, or a parsed attachment. If that processing code has a flaw, a crafted message can run code as soon as the device receives it. A one-click exploit is the form that waits for a tap, usually on a link sent by SMS or a chat app. iMessage has been a common zero-click path because it parses messages in the background.
Relevance
On a phone, the usual entry is a system app that parses data before anyone opens it. Obfuscation and an anti-cheat watch the game process. An OS update is what closes a zero-click flaw once the vendor has patched the parser.
Example
A phone receives an iMessage built to hit a flaw in the parser. The system builds a preview and the flaw runs code. The user never opens the thread. The same payload sent as a link in SMS would have waited for a tap.