There is one Radio Shack "learning kit" that I recommend, but this one isn't it. However, the purpose of this "lesson" is to teach you some of the properties associated with all relays: namely pull-in voltage and current, and drop-out voltage and current. There is a 9V battery and two series-connected 1.5 V cells forming a 3 V battery, all located in the lower right corner of the breadboard. The 9 V battery has its positive terminal connected to terminal 120 and the negative terminal connected to terminal 121. The two 1.5 V series-connected cells have their positive terminal connected to terminal 122 and their negative terminal connected to terminal 123. Depending on how you connect these two voltage sources in series, you can obtain 6 V (series opposing) or 12 V (series aiding).
The relay coil is apparently rated for a minimum of 3 V DC, but the explanation for that is poorly written. Quoting from the page image, "The Relay used here has a resistance of about 500 ohms and requires a minimum of 6 mA (milliamps) to initially pull the armature (the moving part) in. This means that the voltage required (minimum) is 0.5 x 6 = 3 volts." This explanation sucks, although the result is correct. The operating equation is V = I x R, where V is measured in volts, I is measured in amperes, and R is measured in ohms. So, plugging in I = 0.006 A and R = 500 Ω and multiplying, we do indeed get 3 V. But a novice wouldn't have a clue where "0.5 x 6 = 3 volts" came from.
As for the "mods" or "experiments"... (1) wiring the voltage sources in series opposing to get 6 V is supposed to show you that this particular relay will definitely pull in (actuate) provided you use fresh cells. (2) Inserting a 100 Ω resistor usually allows the relay to operate from the 6 V source. WTF does this teach you? Nothing, IMHO. Now try the 9 V battery alone? You know it works with 6 V, so what does operating it from 9 V teach you? Try operating from the 9 V supply with first a 470 Ω resistor and then with a 1 kΩ resistor in series with the relay. What did you learn from that? The relay probably operates with the 470 Ω resistor, but fails to operate with the 1 kΩ resistor? So what? (3) Insert a 1 kΩ resistor in series with the Relay and then (4) momentarily short circuit across the 1 kΩ with a piece of wire. You may already have the 1 kΩ resistor inserted in series with the Relay from experiment (2), so what (4) is asking you to do is deliberately place a wire across this resistor, effectively removing it from the circuit and replacing its resistance with the very low resistance of the wire. This temporary connection works, but to advise a novice learner to deliberately create a short-circuit seems to me to be bad instruction. What experiment (4) is trying to teach you is the relay will actuate with 9V and zero resistance and will stay actuated when the zero resistance is suddenly replaced with 1 kΩ resistance by removing the shorting wire.
If none of this is clear to you, I suggest you start with a very basic instructional text that teaches fundamentals of electricity and electric circuits. Performing "monkey see, monkey do" tasks where you connect wires to various components will teach you absolutely nothing of value. And purchase an inexpensive digital multi-meter from one of the big-box home improvement stores. You cannot learn about electricity (or electronics) without making electrical and electronic measurements. You may be able to build a house with only a hammer, nails, and wood but a tape measure would certainly help keep things sorted. The multi-meter is the electrical and electronic equivalent of the carpenter's tape measure. Buy one and learn how to use it. Most of all, have fun!
