Seems like you never learned the electrical basics. Short explanation :
Series : The most basic circuit.
If you try to make a circuit like that running on for example 6volts AC with 3 10v light bulbs, you will notice that the light bulbs will not glow very much. And if you remove a light (or if it burns) the circuit is cutted, closed, no more current is passing.
Parallel : ''Safer'' circuit, a bit more complicated but it is logical.
Here, the power is equal everywhere, meaning that if the circuit is running 5V the current will be of 5V everywhere. You will probly have to use one resistor for each LEDs if you are not using the same leds in the circuit, or one big resistor for the lot; but don'T trust me for resistors, I dont know how they works, and how to use them. So as you have read in the first post formulas ^^^^ each LED will be using its own voltage and amps settings. Basically, 3 6V bulbs made for 10V will light at 6V full efficiency (like if you would only be using one 6V bulb on series). But this circuit can be a bit more dangerous, if you happen to make a shortcircuit error (like removing a light and just tie the wires together), if you ahve nothing on the circuit that will eat a bit of power then itll shorten.
I sucks for explanations, but its about that for series and parallel. Just tell me if I said something wrong, but its hard to tell everything in english (im originally french, and still not perfecly bilingual).
Hastly said :
Series uses less power, but the lights wont show up as brighly as if they were linked in parallel. Parallel allows your leds to bright as they would normally, and the circuit won't close if one LED closes.