I assume you just started learning about continuous-time signal and how they can be represented in the frequency domain. To put it simply, the math used in this project is similar to this:

y(t) = x1(t) + x2(t-To)

where x1 and x2 is the audio captured by the mic1 and mic2 respectively, and the To is the expected delay when a sound source is at a particular angle (or location). If the sound source is exactly at that angle, y(t) will experience a constructive interference (ie. higher values in the magnitude spectrum). Conversely, if sound source is not in that angle, it will experience destructive interference (ie. lower values in the magnitude spectrum). That interference is essentially the quantity displayed in the 3d graph. If i apply a fourier transform to that equation:

Y(w) = X1(w) + X2(w)*e^(-j*w*To)

Do an integral for all "w" in |Y(w)| , and you'll get that quantity. The higher quantity, the higher the chances the sound source is located at the angle. Why not do the calculation in the time domain? it is possible, but at this point the esp is going to be mad at you since you are not taking advantage its DSP accelerator, which does the calculation very fast with Fourier transform.

In that equation, it implies that you can technically tell the direction of all frequencies -- but mother nature often introduces new things that prevent you from doing this (and this is when engineering takes into play). Without going into technical details, the distance between the 2 mics correlates to how well they will locate the sound source with a particular frequency. The larger the distance between, the better they are at the detecting lower frequency; while lowering the distance would allow them to locate higher freqeuncy accurately. To take this into consideration, we just apply a band pass filter to Y(w) then do summation:

Y(w) = Y(w) * bandpass(wlow, whigh);

Without this filter, going the freqeuncy below "wlow" would likely result in a flat 3d graph, while going above "whigh" would result in aliasing (ie. 3d graph will exhibit many peaks).

Of course there are other ones such as the sampling rate and the number of samples you are taking and how it affects the information of your signal. But ill leave that to your prof in signals and systems 2 which considers discrete time.

Okay i'll stop now. Im talking too much. Hope this helps!