In this case it is an idiom that is used in response to a rare or surprising event. "Where on earth" could be in response to a surprising object such as "where on earth did you get that?" (implying it is strange and not common or difficult to imagine where it could be from). "What on earth" could be in response to a surprising event, such as "what on earth is happening?" "Why on earth" is also possible, such as "why on earth are you here?" in response to someone showing up to an event you told them not to come to. The addition of "on earth" simply adds an extra layer of surprise or confusion than why, where, and what would on their own. They all can have positive or negative connotations depending on the meaning.

As grace said, it is used to express surprise, shock, or incredulity to something. "What on earth" has the same meaning as "What the hell" or "What the f**k" in a sentence like "what on earth is that?", but is less rude.