Coroutines allow writing asynchronous code in a sequential manner by suspending execution until an asynchronous operation completes. The document discusses how coroutines can be used to simplify asynchronous code for an order processing use case that involves retrieving user, address, product, and store data from repositories. It shows how coroutines eliminate nested subscriptions by suspending until asynchronous operations like retrieving a user or address complete before continuing execution sequentially. The Kotlin compiler converts coroutine code into recursive functions implementing a finite state machine to simulate sequential execution across asynchronous operations.