The important thing to me is to distinguish between the abstract concept of asynchronism and how it can be implemented, and by the latter I mean both at the abstract level of a programming language and by technical coordination means in a machine. For the abstract concept at the highest level, well, it is just the dual of synchronism: two (or more) parties that somehow need to work together (i.e., one has a dependency on the other in a way that certain things need to happen before another one can continue) are not synchronized, meaning that it is not known or not defined when the things that need to happen after something else will be done. Seen that way, this definition is not hard. The hard thing can be the abstract means designed in a language: the amount of cognitive effort it takes in order to comprehended them and/or use them (in an fault-free way).
Largely agreed: async means that the code is structured in such a manner that the only way to be certain that a task is complete is to perform some rendez-vous. By extension, it covers mechanisms to make this happen in your code.
