Circa 1762, a guy named Robert Lowth published his assertions of how the English language should be used. Throughout the century, other academics like John Dryden released their own grammars, all based on the venerable model of Latin, which of course has its perks. Among the rules stridently defended by the men was the preposition rule most of us since have learned. That is, never to leave a preposition hanging on at the end of a sentence. (Many people obey this rule but ignore its more specific extension that prepositions should not be left at the ends of phrases within sentences.)
Now, the main reason these fellows got ants in their pants over prepositions was because of the name given to these pesky parts of speech. "Preposition" (or, in Latin, something like "prepositorioeummum," I'm sure) means "positioned before." So old Lowth and Dryden and their bewigged buddies figured that if Verjanusillium and his Roman cohorts kept their prepositions in the fore, it must be the best thing to do in English as well. And so they wrote carefully-worded treatises dedicated to the matter and convinced their schoolmaster friends to beat the rule into students, and beatings are now forbidden at school, but teachers still enforce the preposition rule without even knowing or caring why.
That would be fine if it weren't harmful. But students today learn that any of the words commonly used as prepositions mustn't be used at the ends of sentences. What about something like "put the shoes up"? When you put the shoes up, are you literally putting them up? Are closets all arranged in such a fashion that shoes, when moved, are put into a spot higher than they had formerly been? Well, no. The problem is that "up" isn't acting as a preposition here. It's acting as a particle of a phrasal verb, "put up." Note that you could say either "put the shoes up" or "put up the shoes." That you can do this is a pretty good test for whether the construction is a phrasal verb or a prepositional deal. It's fine to have "up" at the end of the sentence in this case, because it's not acting as a preposition at all, but kids don't learn this. Not that being aware of the fact is all that important, but I'm considering principles here, slovenly teaching that leads to misinformation and ignorance.
The other problem with the preposition rule is that it tampers with clarity. If language were all about following pretty sets of rules, then we'd have no problem; but it's about communicating clearly. And if you get bogged down saying things like "That is the closet into which I wish you to put the shoes of which we just spoke," your syntax muddies your message.