i think i'll probably be corrected on this, but this is my understanding.
when you play a low Bb, the note you hear is actually a compliation of many different frequencies. in some instruments, some of the notes are more prevalant than others, but every different kind of instrument (not individual horn) is different. that's one of the things that makes up the quality, or tone of the sound. when someone says overtone, they're talking about all those extra frequencies above (not below) the note that you're actually playing. as far as i know, they start off an octave above the original note, then a fifth above that, then up to the second octave above the original note. once you get way way way up there, the frequencies will move in every half step (not too sure about that).
so why do we want to practice playing overtones?
because altissimo is basically just that, overtones. the fingerings for altissimo, if they're a weird fingering not in any normal note, then i've heard them described as being a 'combination' of more than one fingerings to create (and i'm guessing on this) an overtone that the two fingerings your'e combining share in common, so it'll pop out easier.
again, i'm probably going to be corrected by someone who really knows what they're talking about, but this is my understanding.
how do we practice overtones?
well this is actually extremely difficult to describe. i actually discovered them on accident and then learned what they were. the easiest one would be to play a low Bb with the octave key. you should just play a normal Bb in the middle of the range of the horn. try adjusting your throat and/or embouchure until you hear it come out. when your'e first beginning, you'll hear the two octaves competing against one another in order to be the prodominant note. this is natural when you're first starting out, don't be deterred by this. when you can play it fine with the octave key in, try to play it without the octave key. stop the tone, release the octave key, and see if you can play the overtone. now see if you can go back and forth between the low Bb and the middle one with the same fingering. after you can do that easily, practice playing each one for as long as you can breathe. take in a big breath and blow until the AIR stops, not when you're about to stop so you stop it with your tongue. let your air just run out. do this with a tuner and try to get each note in tune quicker and quicker and stay perfectly in tune for the entire duration. next try to do the fifth above that. by now, with all this practicing, you've probably already done it on accident. it should sound like your normal second octave F. just try to get it with the same consistency, going back and forth, jumping around from note to note until it's all perfect, with long tones, pitch etc. then you can keep going up and up and up.
this, by the way, will not happen over night. if you're as dedicated as you sound, it should take you a few days to a couple weeks before youc an get everything perfect like i've described.
again, i'll probably be corrected, but this is just my understanding of it.