Some basic equations, markings, technical terms and so on. It should explain everything you can find on this website. If not, tell me, I'll fix it.
(European symbol set as used around this website; other countries may have different standards)

Resistors are usually small, thickended cylinders. It's hard to print numbers on such shape, so the resistance values are coded by coloured stripes. Meaning of the colours is shown in the table on the left, possible combinations are:
Order of the stripes may be tricky to figure out. First stripe is usually closer to the end of the resistor than the last one, or the last one is placed further apart from the rest. If all of them are spaced uniformly, the gold or silver is last  these colours can only appear as exponents or tolerances. If gold or silver is not present, we must measure the resistance ourselves. 
Because we are too lazy to write decimal points and Greek letters, resistances and capacities have a special shorthand syntax where the unit code is used instead of the decimal point. For example, 1R5 is 1.5 Ω, 15R is 15 Ω, 1k5 is 1.5 kiloohms, 3M is 3 megaohms and so on. Capacities are similar, but because one farad is rather big, we shift the decimal point four orders down so that picofarad becomes the basic unit: 10C is 10 pF, 10k is 10 nanofarads (nF), 3M5 is 3.5 microfarads etc..
Resistor is a pure ohmic resistance, current grows linearly with applied voltage. The only two parameters we care about is resistance value and maximum power.
Incandescent light bulb is also a resistor, but its resistance grows with filament temperature. So it is selfregulated: if we apply more voltage, the current grows too, but not as much as with a conventional resistor. If we apply too much, the filament blows. With smaller voltage the light is weaker and less efficient (the greater the filament temperature, the more power gets converted to visible light; the rest is infrared).
Diode only conducts electricity in one direction. Ohmic resistance in the conductive direction is negligible, there is just a slight voltage drop (several tenths of a volt). Resistance in the nonconductive direction is infinite, just be careful to not exceed maximum allowed voltage  if you do, the diode gets destroyed.
LED (lightemitting diode) behaves similarly: it has little to no ohmic resistance in the conductive direction, it just eats several volts of the input voltage. The rest runs through it without limits, so if we don't want to burn it, we must put a suitable resistor in series with it. Before we exceed the LED's threshold voltage, it doesn't shine at all. In the nonconductive direction, it can survive much less than a classic rectifier diode, so it is not suitable for AC power.
Zener diode works the same as a normal diode in the conductive direction. In the other direction, it starts to conduct when the voltage reaches its threshold value. This threshold is almost currentindependent, so ZD are useful as voltage stabilizers. The only limit is the waste heat that must be dissipated safely.
Coil is to electricity what a heavy turbine is for water: if we apply voltage, it resists it for a while, but when it spins up, the resistance disappears. If we close the valve or disconnect a wire, inertia of the turbine or magnetic field keeps pushing the current through for a while. A coil can therefore generate a dangerously high voltage that can throw arcs and destroy semiconductor components. That's why we need to connect antiparallel blocking diodes: the unused current needs a path to run through and discharge.
Capacitor behaves like a dam: it doesn't let direct current through, it just accumulates a charge that can be returned back to the circuit later. A charged capacitor can generate high currents capable of destroying sensitive components (just like a breached dam), so be careful what you connect to its terminals.
On a bike, we find alternating current on the generator output terminals. Usually we either feed it to light bulbs directly or we rectify it before further processing, so I'll be brief.
Basic property of AC is that it constantly switches its polarity. The frequency depends on our riding speed. Voltage looks mostly like a sinusoid. Its effective value (like those nominal 6 V written on the alternator) is calculated as maximum amplitude (height of the wave tip) divided by square root of two (1.414 and something). This means: if we take an alternating voltage, rectify it and pour it into a capacitor, we get a DC voltage 1.414 times larger than the effective voltage  for example, 6 V AC becomes 8.5 V DC.