A preposition is a word that indicates a "relationship" between a noun (its object) and some other part of the sentence. A preposition usually comes before the noun it relates to. In some languages, such as Japanese, such words come after the noun and are called postpositions.
Example: The train goes along the line under the bridge, through many towns and arrives at the final station, on time, with many passengers on board.
In many languages, one can not use a preposition to end a sentence with--that is to say, it is impossible to move a preposition's object away from the preposition itself, as has been done with a preposition in the first half of this sentence. English is an exception, allowing both so-called preposition stranding, as in What did you open the jar with? and pied piping (that is, moving a preposition and its object together to the beginning of a sentence), as in With what did you open the jar? Many schoolteachers and editors discourage writers from stranding prepositions, and preposition stranding has long been thought to constitute poor style in English writing. (Even the strictest schoolteachers and editors, however, would acknowledge that it is not necessarily poor form to end a sentence with a preposition that forms part of a compound verb such as see off or run over.)
Winston Churchill is reputed (though there is no definitive authority on the quote) to have noted, in reference to the practice of banning the ending of sentences with prepositions, "This is the sort of English up with which I will not put." His point, it would seem, was that an injunction against ending a sentence with a preposition, can, if slaveishly followed, lead to stylistic disasters.