I've not completed the project, but I may be able to lend a hand.
From the list of components you give, you don't seem to have an LDR (Light Dependent Resistor). However, the green LED that you do list is still needed here, just elsewhere. For this tutorial, the LED should be connected to the board as it is for the blink programme, so you are on the right track here.
To answer your question, an LDR is not the same thing as an LED (Light Emitting Diode). An LDR is like the 10k ohm resistor but its resistance varies with the amount of light falling on it. They typically have a high resistance in the dark (a few megaohms) and a lower resistance in light (a few kiloohms), depending on the brightness of your light source. I've found the following links to show you what an LDR looks like: LDR picture 1
and LDR picture 2
. These two pictures may not look that similar but the difference between them is mostly due to how the sensor is packaged. To connect the 10k (see ) resistor and the LDR to the board correctly, connect one leg of the LDR to the "5V" pin, the other leg of the LDR to the 10k resistor and the other, free leg of the 10k resistor to the "GND" pin. Now connect the junction made between the LDR and the 10k resistor to the "A1" pin.
To answer your other question, there are two things going on here with the 10k resistor and the LDR (see ). The first thing is that the 10k resistor will set the maximum current that can flow through the LDR (and itself). If the LDR were in very bright light, its resistance would be close to zero and therefore the current through the LDR would be nearly equal to 5 (volts) divided by the resistance of the ordinary, invariable resistor. Using a 10k resistor here gives a maximum current of 0.0005 amps (or 0.5 milliamps), by Ohm's Law (V = I * R). As there will also be a voltage drop across the LDR (more on this later), the voltage dropped multiplied by the current will give the amount of power the LDR has to dissipate (P = V * I). As this power is dissipated as heat, too much and the LDR will be damaged or even melted/burned. Hence, careful selection of the value of this invariable resistor will protect the LDR. The second thing (hinted at earlier) is that the two resistors will divide up the 5 volts that you have put across them in proportion to their resistances. Hence, this circuit fragment is called a voltage divider
(or potential divider, see the link on how they work). As the resistance of the LDR changes with the amount of light that shines on it, the voltage at the junction between the LDR and the 10k resistor also changes, as a result of this voltage division. As this voltage is sensed by the board at pin "A1", you now have a light level sensor to which your Arduino can be programmed to respond.
I hope this helps, sorry if you know any of this already but as you say you are starting out, I thought some detail was appropriate. Enjoy your adventures with Arduino and let me know here how you get on.
All the best,
 As resistance is always measured in ohms, electronic engineers usually omit this (the unit) in circuit diagrams and just give the number and a multiplier of the value of the resistor, so k = kilo, 1,000; M = mega, 1,000,000 etc., thus 10k is 10,000 ohms.
 Resistors are known as passive components and as such just do what their resistance value (and ability to dissipate heat) dictates. They don't "work" as such. That blob (some sort of plastic or resin) in the middle of the "wire" contains the resistance and the two legs (both good conductors) connect to either end of the resistance. It only looks like a blob on a single piece of wire.