Quick, What's A Preposition?

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​QUICK, WHAT'S A PREPOSITION?

        Yesterday I was giving a young acquaintance some online help with her grammar homework. The assignment involved learning to identify verbs, adverbs, pronouns, and prepositions and to differentiate one from another. 
         To this end, the students were given a sheet of paper on which a variety of words were superimposed over a coloring book page which could be colored in after each of the words had been written on a line in the correct word category column at the top of the page.

         Before we started the exercise I wanted to make sure my young friend was clear on the definition of each word category. 
          A verb, I explained, is an action, something that you can do. An adverb is a word that tells how or when you're doing the thing you're doing. A pronoun is a word you use for a person or thing  when you're not using their name, like I, you, he, she, it, we, you, and they, this, that, these, those. But, I expanded, pronouns can also be used when you're talking about something that belongs to someone, like my, your, his, hers, its, ours, their, theirs. 
       "I know about all those!" the child interjected.  "But what's a preposition?"

    "Well," said I, "a preposition is..." And I drew a blank. I could not explain what a preposition was.
      Which, ironically, is not to say that I wouldn't know a preposition if I saw one. In fact, what I have to say about propositions is along the lines of what United States Supreme Court Justice Potter Stewart had to say about obscentiy in the 1964 case of Jacobellis v. Ohio, in which a movie theater owner in the town of Cleveland Heights was convicted on obscentiy charges for showing the film "Les Amants," the award-winning 1958 masterpiece of French director Louis Malle.

​     The case made its way up to the Supreme Court where the justices decided that, though the movie might be a little much for Cleveland Heights, Ohio, it really wasn't all that bad, in fact they thought it was a pretty good flick, an opinion with which Rotten Tomatoes has more recently concurred, giving "Les Amants" (The Lovers" in English) a 90% rating.

    It was while adjucating this case that Justice Stewart gave his famous opinion on the test for obscentiy: he couldn't really describe it, but he knew it when he saw it.
       Anyway, that's me and prepositions. I can't describe one but I know one when I see one, thanks to Sister Mary Aquinas, my sixth grade teacher who required her students to memorize the prepositions, which I dutifully did and remember to this day:

​The Prepositions
 About, above, across, around, at,
Before, behind, beside, between,
 By, down, during, except for from
 In, into  near of off on,
  Through, to, towards, up, upon, under, with

      As for helping my young student, instead of attempting to define prepositions, I just recited  the list. Whenever we came across a preposition on the word page, I recited the list again. After a few recitations the child was able to identify the remaining ones on their own, saying, "I remember it from the list." And so that took care of that.
​      I still don't know what a preposition is, though of course I could easily find out in an internet minute. But I've decided not to. Sometimes it's more fun to learn something organically, or just not know it.
        And so, to that end here is my question: Does anybody know what a preposition is?