Simply said asynchronous execution is doing stuff in the background.
For example if you want to download a file from the internet you might use a synchronous function to do that but it will block your thread until the file finished downloading. This can make your application unresponsive to any user input.
Instead you could download the file in the background using asynchronous method. In this case the download function returns immediately and program execution continues normally. All the download operations are done in the background and your program will be notified when it's finished.