Ok, let's start with the old standby, the Surefire G2 incandescent flashlight. Picture the G2 as a metal tube containing an incandescent bulb, two cells stacked one on top of the other, with a switch at the far end. Now, the cells contain a material that loves to give off electrons. Being negative, the electrons cluster at the negative pole of the cell. The neg pole of the bottom cell is connected to the switch at the end of the light. When the switch is closed, the electrons stream out of the negative pole of the bottom cell, through the switch, and travel toward the lamp at the other end of the light by flowing through the metal tube. One connector for the lamp is connected to the metal tube, and allows the electrons to try to flow through the lamp filament. But the filament really doesn't want to let the electrons through. So in order to make it through the electrons have to push the metal atoms around, causing them to get hot enough to emit light. The by now tired electrons fall down through the center electrode of the lamp assembly to the positive connector of the top cell. Now this end of the cell is positive because all of its electrons are down at the other end of the cell. So the electrons coming in the positive contact mix with the positive stuff and switch it back to neutral. But the contents don't really want to stay neutral, so the electrons once again take off for the negative end of the cell. Now the negative end of this cell is connected to the positive end of the cell below it, so the same process occurs again. The end result is that the electrons continue to pile up at the negative contact of the bottom cell, and flow through the circuit again and again, as long as the switch is closed.
So now let's replace the incandescent bulb with an LED. The only difference is that the LED takes the electrons in and use them to make light more directly, without most of the heat associated with the incandescent filament. So more light is given off by the same amount of electrons. Everything else remains the same.
The amount of push each cell gives the electrons as they leave is controlled by the material the cell is made of, and is called 'voltage'. When the cells are connected negative to positive, or 'in series', the voltage pushes add up and push the electrons harder, like having two engines on a train instead of one. The number of electrons each cell contains is controlled by the amount of material in each cell, as well as the material composition. The more material in a given cell, the greater the number of electrons available. The number of electrons that pass any point in the circuit in a given amount of time is called the 'current', and is measured in amps. Since the electrons have to pass through any and all cells that are in 'series', the total number of electrons available at any given moment remains the same, regardless of how many cells there are.
If the cells were connected 'in parallel', where all the positive electrodes were connected to each other, and all the negative ones as well, all of the electrons would only receive a push from one cell, so the voltage would remain the same, regardless of the number of cells. But because all of the cells are able to make their electrons available at once, the total number of electrons available to work at any given moment will be the sum of the electrons available from each cell, so the 'current' available increases. Thus ends Flashlights 101.