Also, if you could tell me a bit more about the overtones (I’m a noob, you know), I’d be grateful.
When you play a note on the flute, what you hear is actually a combination of notes.
The lowest note–the one you are fingering and “aiming for”–is called the fundamental.
There are notes above it that are called partials or overtones.
Depending on the flute–and later, depending on what kind of tone you are playing with–there may be less or more of some of these partials.
When you jump the octave from the first octave to the second, you are really doing nothing more than jumping to the first partial.
You can keep going higher and higher–again, depending on the flute and the strength of your embouchure–up and up through the sequence of notes called the harmonic series.
The harmonic series is best described with math. 
If f is your frequency of your fundamental, then your first octave is going to be 2f. 3f is going to be the perfect fifth, 4f is going to be the octave again (really, up a perfect fourth). And so on…
One way really good flutists can change their tone at will is by altering the strength of the overtones verses the fundamental.
A sound with lots of overtone content on a wooden flute will sound almost like an oboe–it’ll have a powerful cutting edge and will be so strong it may almost be unpleasant to listen to.
A sound with little overtone content is rounder, sounds more “relaxed” and doesn’t have that cutting edge…a “woodier” sound.
Too little overtone content, and your playing will sound wimpy, washed out, and lifeless…too much, and people will wonder why you are pissed off all of the time. 
For a learner, the challenge is to be able to predictably get a good, strong, clean sound…one good tone that they can hit predictably. The bit about being able to change tones on the fly isn’t something to worry much about till you’ve been playing for several years.
–James
