I can't understand what this function aio_fsync does. I've read man pages and even googled but can't find an understandable definition. Can you explain it in a simple way, preferably with an example?
aio_fsync is just the asynchronous version of fsync; when either have completed, all data is written back to the physical drive media.
Note 1: aio_fsync() simply starts the request; the fsync()-like operation is not finished until the request is completed, similar to the other aio_* calls.
Note 2: only the aio_* operations already queued when aio_fsync() is called are included.
As you comment mentioned, if you don't use fsync or aio_fsync, the data will still appear in the file after your program ends. However, if the machine was abruptly powered off, it would very likely not be there.
This is because when you write to a file, the OS actually writes to the Page Cache which is a copy of disk sectors kept in RAM, not the to the disk itself. Of course, even before it is written back to the disk, you can still see the data in RAM. When you call fsync() or aio_fsync() it will insure that writes(), aio_writes(), etc. to all parts of that file are written back to the physical disk, not just RAM.
If you never call fsync(), etc. the OS will eventually write the data back to the drive whenever it has spare time to do it. Or an orderly OS shutdown should do it as well.
I would say you should usually not worry about manually calling these unless you need to insure that your data, say a log record, is flushed to the physical disk and needs to be more likely to survive an abrupt system crash. Clearly database engines would be doing this for transactions and journals.
However, there are other reasons the data may not survive this and it is very complex to insure absolute consistency in the face of failures. So if your application does not absolutely need it then it is perfectly reasonable to let the OS manage this for you. For example, if the output .o of the compiler ended up incomplete/corrupt because you power-cycled the machine in the middle of a compile or shortly after, it would not surprise anyone - you would just restart the build operation.