Coroutines are functions that can suspend their execution and resume it later on. They allow writing asynchronous code in a very similar manner to how you would write synchronous code. Compared to writing asynchronous code with std::async, this allows writing cleaner code that's easier to understand and maintain. There's no need to write callbacks anymore, and no need to deal with the verbosity of std::async with promises and futures.
Aside from all that, they can also often provide you with much better performance. std::async based code usually has more overhead for switching threads and waiting. Coroutines can resume and suspend very cheaply even compared to the overhead of calling functions, which means they can yield better latency and throughput. Also, one of their design goals was to be highly scalable, even to billions of concurrent coroutines.
