What does" How on earth did you do it?" mean?
I guess "on earth" has a special meaning here, am I right?
Please help me to explain the meanings about the phrase and the sentence!

Thanks a lot!Thank you very much for helping me, thank all of you!

Question

What does" How on earth did you do it?" mean?
I guess "on earth" has a special meaning here, am I right? 
Please help me to explain the meanings about the phrase and the sentence!

Thanks a lot!Thank you very much for helping me, thank all of you!

Answer

When something is not very probable, but you did it anyways... HOW ON EARTH DID YOU DO IT??? what were the chances for this to happen? 
If you delete "on earth" you will have a common, normal daily expression... but if you add "ON EARTH" you are giving to the question the surprise and "oh God, I don't believe it " factor .
^^

Answer

I think maybe it is  how could you know who are you and what you should do,or what can you contribute to our home -earth.

Answer

It just means:

"How did you do it?"

The "on Earth" is used for emphasis, perhaps to show surprise or disbelief on the part of the asker.

Answer

I think it's referring to something that a person didn't know could happen. I believe the "on earth" is just used to exaggerate that surprise.

Answer

the Chinese meaning of "on earth" here is: "究竟"“到底”。整个句子：你到底怎么做的？