Grammatical usage err that occurs when a preposition is left at the end of a sentence or clause. This idiom of the English language is the result of a famous writer's* decision to translate of his poems into Latin and then back into English. In doing so, he found that it was impossible to end a sentence with a preposition in Latin, and therefore must be incorrect in English.

Some examples are:

• What are you looking at; should be "At what are you looking?"
• What are you thinking of (and/or about); "Of what are you thinking?"

Doing this, however, gives a very stilted and archaic feeling to writing/speaking, and as the English language evolves, many editors, professors, etc. are accepting dangling prepositions as natural and correct.

*I believe the writer was John Donne, but I am currently checking the reliability of my source