Welcome to Ham SE, @Newbie, and thanks for your question.
If you break a length of wire to create two terminals and apply an AC voltage across the terminals, you will excite an alternating current on the wire. Some wire lengths will accept more power from the generator than other lengths.
The antenna cited in your reference has two terminals but, because Ground has some electrical conductivity, one of the two terminals is actually the Ground under the "$\lambda$\4 radiating element":

The ability of the "antenna" - in this case, the combination of the radiating element and the ground underneath it - to accept power from the generator depends on how much the antenna resists the flow of current. When speaking of AC voltages, we call this Impedance, symbolized by the letter Z and measured in ohms just like resistance for DC. For a given generator voltage, more current flows on the antenna when the Impedance is lower. When more current flows on the antenna, stronger electromagnetic waves are radiated.
The impedance at the terminals - the "feedpoint" - varies with frequency. If we make the antenna 5-meters tall, the impedance seen by the generator will follow the green curve in the graph below as we change the frequency of the generator:

Notice that the antenna has the least resistance to the flow of current - the lowest impedance - at about 14.35-MHz, so this is the frequency at which the most current will flow and the strongest electromagnetic waves will be radiated.
In free space, the length of an electromagnetic wave, $\lambda$, is:
$$\lambda = \frac{c}{f}$$
where $c$ is the speed of light (300 million meters/sec) and $f$ is the frequency of the generator (Hz). At $f$=14.35MHz:
$$\lambda = \frac{3*10^8}{14.35*10^6} = 20.9-meters$$
So, our 5-m tall antenna is approximately 1/4 of the free-space wavelength of the 20.9-meter signal applied to the antenna terminals.
The reasons the antenna is not exactly $\lambda/4$ are beyond the scope of your question. Antennas like this "quarter wave vertical" are indeed popular, but often for a complex set of reasons - cost, available space, materials on hand, stealth, etc. - not simply its "performance."