Then SomeAsyncMethod has to block the program in some way
No, it doesn't. It's asynchronous. The definition of what it means to be asynchronous means that it doesn't block; the caller will continue on after the method returns, without it having done its work, and the work will be completed at a later point in time.
it will have to interrupt the program at some point so that it can run SomeAsyncMethod. Right?
No. It's asynchronous. It may not even be work that needs to be performed by a CPU at all.
Let's go with an analogy here. You order a package. Are you prohibited from ever doing anything until that package arrives? Are you forced to sit in front of your house explicitly waiting for that package, incapable of doing anything else until it arrives? Or can you go off, do other work, and then at some point in time, when the package arrives on your steps (not necessarily immediately, you can go pick it up at any arbitrary point after it has been delivered) you can open it up and do whatever it is you needed to do with what you ordered.
This is an inherently asynchronous operation. You start the asynchronous operation (order something) then you can do whatever you want until the operation you started is completed, without it occupying your time at all, and then at some point in time, after the operation has finished, you can use the results of that operation.
One type of asynchronous operation that you can perform when programming is asking another thread to do some CPU bound work, and that work may (or may not) be performed on a second processor, but there is all sorts of other types of asynchronous operations that need no other processors, such as IO (performing a network request, for example) which is virtually always inherently asynchronous, and lines up pretty nicely with the "order a package" analogy, there's performing an action after some trigger (an event, etc.), you can have an asynchronous operation that is itself composed of one or more other asynchronous operations, etc.
See this post for another example explained in a bit more depth.