SYNCHRONOUS:

Synchronous sound represents the matching of sound to the movements that are taking place on the screen. For example, if you see a person moving across the screen, perhaps walking in water, then you might hear footsteps and you could also hear splashes as each step is taken.

ASYNCHRONOUS:

Unlike synchronous sound, asynchronous sounds in film do not necessarily correspond with what you see on the film screen. Asynchronous sounds in film can still add value to the action being performed, but it’s likely an action that already took place (such as a previous sound) or the sound of an action that is about to occur on the screen.

(source – beverlyboy.com)