How do coaxial cables carry information that a TV can intercept and display?
This wikipedia article covers most of the aspects of how analog television works: http://en.wikipedia.org/wiki/Analog_television

I will give a brief summary, though.  

The picture is formed with a series of horizontal scan lines.  Sometimes you will see TVs or cameras advertized with a certain number of 'lines' of resolution - this is why.  You don't get pixels until you're talking about a digital signal.  The lines are transmitted serially one at a time.  In the days of CRT televisions, the lines would be sent to the electron guns in the TV as they arrived and the electron gun would draw the line on the screen.  Nowadays, the TV just digitizes the signal and dumps it in a buffer.  

Audio and video are transmitted as two separate signals.  In the case of cable TV and broadcast TV, both signals are modulated onto carrier waves, with different carrier waves for each channel and a known offset between the video and audio carriers.  Then the TV can tune into a channel just by picking the correct video and audio carrier frequencies and demodulating the signals.