Impedance matching. The point of the capacitor is to load the loop so it becomes resonant; the loop's reactance is much less than the impedance of free space, and intercepts less than a wavelength around, so its radiation impedance is even higher (or lower) still, compared to the impedance of space.

Whether it's higher or lower, depends on the equivalence being measured. The series and parallel equivalents are related by the resonant circuit: EPR = Zo * Q, or ESL = Zo / Q. Zo is the characteristic impedance of the tank, Zo = sqrt(L/C), while Q is the quality factor.

If we connected our transmission line in series with the loop, we would ruin the Q, and get very little signal out (the radiation resistance, as ESR, might be a few ohms). Conversely if we connect in parallel with the capacitor, the same happens (radiation EPR might be ~kohm?).

However if we use a smaller second loop, we can tap off some of the larger loop's energy, maintaining its Q (actually, dropping it by half, so that the transmission line loads it equally to the radiation resistance -- this comes from the power matching theorem). The equivalent circuit is a nonideal transformer, two dissimilar inductors with some coupling. We again draw the equivalent circuit, which with the right ratio and coupling, gives an ESR of 50 ohms at the feedline -- just what we need.

In practice, it may well be that it's not easy to calculate the dimensions of that transformer (the secondary inductance and coupling factor), in which case additional matching components may be desirable. At this point there isn't really much difference between using an incorrect sub-loop and matching, versus matching the main loop directly. Or the match is considered "good enough" and that's that.

These loops are usually used for receiving low frequencies, where atmospheric noise dominates over antenna losses, even for very compact antennas, or poorly matched ones. A sensitive receiver may still be required, but these are easily constructed with modest transistors, or even op-amps. A better match is desirable for a transmitter, however, as is a larger antenna in general.

Tim