Synchronous Execution
My boss is a busy man. He tells me to write code. I tell him: Fine. I get started and he's watching me like a vulture, standing behind me, off my shoulder. I'm like "Dude, WTF: why don't you go and do something while I finish this?"
he's like: "No, I'm waiting right here until you finish." This is synchronous.
Asynchronous Execution
The boss tells me to do it, and rather than waiting right there for my work, the boss goes off and does other tasks. When I finish my job I simply report to my boss and say: "I'm DONE!" This is Asynchronous Execution.
(Take my advice: NEVER work with the boss behind you.)