Here are the basics as I understand them:
When you play a note in the regular overtone series (See iiipopes above for the BBb tuba open series), the note that your lips are buzzing is amplified by resonating in the tuba
along with overtones also being produced by your lips. Your brain hears all of it, but mostly the overtones.
When you play a note that's considered 'false' or 'privileged', the fundamental note that you're buzzing is not actually amplified. The overtones that you're buzzing are still amplified by the tuba and that's what you hear.
On instruments with 'good' false tones, the right overtones are amplified well. Your brain does a lot to interpret sound and you can't really tell that the fundamental note isn't being amplified.
On instruments that aren't good with false tones, some of the necessary overtones are also not resonating in the tuba. My tuba is like this - if I try to play EEb without using 1+4, it just sounds like mush coming out of the bell. Change to 1+4 (with only a little bit of tube pull), and that EEb speaks clearly.
Edit - Keeping it even more basic -
If the note is being played with any one of these fingerings (see fingering chart -
http://www.olemiss.edu/lowbrass/studio/ ... gering.pdf), then it's not a false tone.
... Except for the low B in the chart that is noted as a false tone