Can someone please explain impedance matching and wave reflection? I'm reading Wikipedia's article on impedance matching (http://en.wikipedia.org/wiki/Reflections_of_signals_on_conducting_lines) and this just seems so foreign to me.
1) What does it mean for a voltage to be reflected bacK? What is physically happening? How can you tell that the voltage has been reflected back?
2) Why does the current reflects an signal with inverted amplitude?
i.e. 
$V = V_+ f(t,z) + \gamma V_+f(t,z)$
$I = I_+ f(t,z)  - \gamma I_+f(t,z)$, what is the physical reason behind the negative sign in front of current reflected back?
3) Why do I never observe this phenomenon in real life? What is the effect of wave reflection?
4) Why do people insist on matching the line to 50 Ohm when the power line above our head is probably hundreds if not thousands of ohms? What component that I use has a 50 Ohm matched load?
Thank you! 
 A: "1) What does it mean for a voltage to be reflected bacK?" 
It means that the wave that was traveling in one direction on the transmission line is now traveling in the opposite direction. 
"What is physically happening?"
Absolutely nothing, and that is exactly what is causing the reflection. The energy in the wave has nowhere to go at the end of an unterminated transmission line, so it has to go back where it came from. 
"How can you tell that the voltage has been reflected back?"
You can easily see it on an oscilloscope. :-) 
"3) Why do I never observe this phenomenon in real life?"
I don't know... probably because you never had an oscilloscope? I was paid a handsome salary for years to take care of these kinds of things in various scenarios and at times I have seen them daily. 
"4) Why do people insist on matching the line to 50 Ohm when the power line above our head is probably hundreds if not thousands of ohms?"
Power lines aren't matched to 50 ohm. Only certain types of signal transmission lines are matched to that value (others are 75 Ohm, 100 Ohm and 120 Ohm, or any other value. I, for instance, have worked with impedances down to a few Ohm in one case). The reason why 50 Ohm was selected as a standard is historical. It could have been 67.8 Ohm, if different pipe diameters had been available to early radio engineers.  
"What component that I use has a 50 Ohm matched load?"
A 50 Ohm resistor. :-) 
A: Let me preface this by saying that I think to truly understand impedance you need to have a firm understanding of electromagnetic waves and their propagation.

*

*When the voltage is reflected back that is because part of the incident wave is reflected back. The reason this happens is that every material has a certain ratio of electric fields to magnetic fields within it. These ratios are similar to the idea of resistance in low-frequency circuits. For example, a low-frequency circuit resistor has a voltage V = IR across it for an input voltage of I. Therefore the resistance of the resistor is a fundamental property that gives the ratio of voltage to current for the resistor R = V/I. In the same way, impedance gives a ratio E/H where E is the electric field and H is the magnetic field. Now when there are two materials with different impedances they also have different ratios of E and H. For this reason, some of the fields must be reflected back so that both materials can maintain their fundamental ratios of E/H. Typically these ratios are determined by the permittivity and permeability of the materials, but in the general case, the structure of the material also has a significant impact.


*The negative sign in front of the reflected current is a matter of convention. γ can take negative and positive values (-1 to 1). So really you could place a positive sign in front of the current but then you would have to negate γ. The value of γ is determined by the impedances of the two mediums


*You have seen this phenomenon in life every day in the form of sound waves. Although not quite the same as EM waves they exhibit many of the same behaviors. For example, you know some materials like hard rocks will cause large reflections (think Echoing) while soft materials like pillows will not reflect noise nearly the same. In electronics, the reason we don't deal with wave phenomena, for the most part, is that it is only relevant at high frequencies or for extremely large circuits (close to the wavelength of the signal).


*50 ohms is used as a standard because it gives a good balance of signal attenuation and maximum power transfer. Not everything is 50 ohms though and you need to know the impedance of the object you wish to deliver power to, so that you can properly transmit the power without large reflections. For example the input impedance of a dipole antenna is generally 73 ohms, so feeding it with 50 ohms would lead to reflections. Similarly if you tried to connect a 50 ohm and 1000 ohm transmission line you would see large reflections.
https://resources.altium.com/p/mysterious-50-ohm-impedance-where-it-came-and-why-we-use-it
