On earth is used for emphasis in questions that begin with words such as 'how', 'why', 'what', or 'where'. It is often used to suggest that there is no obvious or easy answer to the question being asked.
[emphasis]
How on earth did that happen?
What on earth had Luke done?
Why on earth would he want to go to such a place?
See full dictionary entry for earth
on earth
phrase [with neg]
On earth is used for emphasis after some negative noun groups, for example 'no reason'.
[emphasis]
There was no reason on earth why she couldn't have moved in with us.
There is no feeling on earth like winning for the first time.
See full dictionary entry for earth
on earth
phrase
On earth is used for emphasis after a noun group that contains a superlative adjective.
[emphasis]
He wanted to be the fastest man on earth.
...the site of the worst ecological disaster on earth.
See full dictionary entry for earth
on earth in British English
used as an intensifier in such phrases as what on earth, who on earth, etc
See full dictionary entry for earth
on earth in American English
of all things
an intensive used mainly after interrogative pronouns
what on earth do you mean?
See full dictionary entry for earth
Examples of 'on earth' in a sentence
on earth
After 60 years on earth, what will she miss most?
Times, Sunday Times (2016)
It was like going back to live on earth after being in rather a horrible other world.
Times, Sunday Times (2011)
What on earth, after all, is the point of sending an artist on to the battlefield?
Times, Sunday Times (2007)
The incident came a week before shuttle Endeavour is expected back on Earth after its last space flight.
The Sun (2011)
And who on earth, after the daily experience we have, can question the probability of a gentleman marrying anybody?