The quick, somewhat metaphorical answer ... have you ever seen one of those old style "player pianos" like great-great-grandma had? They had rolls of paper with holes punched in it, and the paper was drawn over a mechanical device that depressed a piano key whenever there was a hole at that spot on the paper -- for example, a long hole toward the left side of the paper might mean a bass whole note, whereas a small hole in the middle might mean a quarter note middle C.
MIDI is kinda like that system of recording music. It's the modern day computer equivalent of the standard defining how those holes are supposed to be placed on the paper, etc. Except that unlike piano rolls, MIDI can also record volume information, pitch glides, etc. It's also a standard for not just how music is electronically recorded as notes, but also for how electronic instruments communicate -- so, you can have the notes recorded in a MIDI sequence on your PC but play it through your keyboard, etc.
Now, what would happen if you took one of those piano rolls and played it on a piece-of-crap piano? It would sound like crap. That's essentially what happens with built-in MIDI softsynths bundled with operating systems; they're just barely good enough to put out recognizable notes, but that's it. But that's not "MIDI's fault" -- it just means the player itself is bad. If you want better examples of what MIDI can do, look at some demos by softsynth vendors. They won't be showing off MIDI per se, they'll be using MIDI to show off *their* products, but it should still be a demonstration that MIDI != crap.
Garritan has some pretty good demos online. Also, if you want to explore MIDI further, you might want to think about getting a basic sequencer/mixer package, like those offered by Cakewalk and similar companies. (I don't work for either company, etc., but have software from both places and use it quite a bit).