Any kind of vibration in air will start sound-waves propagating. If the vibration is regular, the sound (pressure) waves will be evenly spaced, and a listener will hear a sound which has an identifiable pitch. If the vibration is irregular, the sound produced will comprise many mixed-up pitches, and the listener will hear a non-pitched sound (noise).
The faster the vibration, the closer together the sound waves will be, and the 'higher' we will percieve the pitch to be. Very low notes are around 40 vibrations, or cycles, per second. The abbreviation for 'cycles per second' is Hertz, or Hz.
At around 260 Hz we are at middle C, and the top of the piano is at just over 4000 Hz.
We can hear, at best, up to 18 000 Hz (or 'sixteen kilohertz' 18KHz... sound engineers refer to this as 18 K etc)
Octaves are a special case: if we double the frequency of vibration, we hear a note that is 'the same but higher'... in other words it behaves similarly in a musical sense, but 'sounds' higher.
So in western music we have divided up the octave into 12 equal steps. These steps are not arbitary but are based on the mathematical relationship between notes and the ratios of their respective pitches: we will not go into that here.
What we as singers do need to know is that as we progress upward in pitch, the sound waves become closer together. That means they become smaller, and that means that everything we do as part of the singing process needs to be more accurate the higher we sing. If we mess up, the voice will break or flip. More of these matters in the section on Resonance.