Inspired by a post by galbinus_caeli about singing off-key.
Sound is a type of wave perceived by the human ear. Sound waves travel through air (or water and other materials) by compressing (squishing together) the air molecules. The air actually jiggles, alternating moving slightly towards and away from you. (If it moved in a big clump towards or away, that would be wind or a breeze.) When the air next to our ear drum gets moved one way and another, the material of our ear drum gets pushed in and out correspondingly. Nerves and the brain then interpret this and we hear things around us.
[As an aside, hearing loss can be caused by damage to the ear drum (as in old age or a "blown" ear drum), or by nerve damage, or by damage within the brain itself. Damage to the ear drum can be fixed I believe, or sounds amplified by a hearing aid. Hearing aids can also be useful for some forms of nerve damage, but not all.]
How "fast" the air "jiggles" is described by scientists as the frequency of the sound wave - technically it's the number of jiggles or cycles per second. Our brain interprets this as pitch. A high pitch is a big number for frequency, while a low pitch is a small number for frequency. Of course, there is more to sound than this.
When a sound is generated by a simple machine (a frequency generator), it will have only a single frequency, meaning the air only jiggles at one rate, and it will sound "simple" or "pure" to our ear-brain combination. This single frequency is sometimes called the fundamental. However, sound (music) is usually created by some (musical) instrument, and this is not simple: we do not get out only one frequency. Similarly to how the ocean has tides, and on top of the tides are waves, and on top of the waves are ripples, sound will have layers of waves. In the water comparison, tides are the lowest frequency, and ripples the highest. In sound, the fundamental has lowest frequency/pitch, and higher frequencies are added on top of it, called harmonics.
When you pluck a guitar string with no fingers on it, the full length of the string vibrates in one lump (called a node). This vibrates the air around it and the human brain most easily perceives this lowest frequency or the fundamental, and we perceive it as the "note" or "pitch." In addition, the string vibrates at the same time in two lumps/nodes, giving the first harmonic. It also vibrates with three nodes, four nodes, and so on. Some of these harmonics vibrate more strongly than others, and which ones depends upon the specific instrument. Most humans don't consciously observe the harmonics, we just put them all together. How strong (loud) the various harmonics are compared to each other and the fundamental is perceived by the brain as the quality or timbre (pronounced "TAM-burr") of the instrument, and what distinguishes one instrument from another (and one person's voice from another).
To change what note is being played on the guitar string, you would then put your finger down somewhere, changing the length of the string, and therefore how fast it vibrates, which means the frequency of sound. For guitars and other stringed instruments, the pitch of each note is also affected by the tension in the string (how tightly the string is wound, changed with tuning pegs) and the density of the string (how thick the string is and what it's made out of, which is why there are multiple strings).
In reed instruments (clarinet, sax), you first vibrate a bamboo or plastic strip, which then vibrates air inside the instrument, and the fundamental is determined by the distance between the reed and the first open hole, and the thickness of the tube of the instrument (that is, the tube the air is traveling through). In wind instruments (flute, piccolo) you're more directly vibrating the air. In most brass (trumpet, tuba) you vibrate a little diaphragm or plate in the mouthpiece and then it follows as above. Percussion instruments you vibrate the material that you're hitting - the face of the drum, wood on the xylophone, cow bell, whatever.
As for what makes a chord, or music, that is cultural, and there's no way I get that, let alone being able to explain it! :-P