I sort of grasp big O notation...but this is sort of over my head like most stuff that has to do with computer or electrical engineering.
As someone who is absolutely terrible at math, I envy the people who grasp or at least can learn this type of stuff and get an engineering degree and license.
All I really know about FFT is that is changes a signal, its somehow used in processing signals of some kind, and it apparently from what I heard was the key to detecting nuclear detonations back in the day.
Having a decent intuitive notion of Fourier transforms is an incredibly useful tool in your toolbox, even if you can't derive a Fourier transform by hand or write a fast Fourier transform (FFT) algorithm.
The basic idea is this: (almost) any (useful) signal can be represented as a sum of sine waves with different frequencies and phases. For example, an electrical signal or a sound wave is a one-dimensional signal where the x-axis is time. This might look like a really complex squiggly line that's hard to work with. Using a Fourier transform, you can separate the individual frequencies of that time-based signal. Then, you can modify the specific frequencies however you want. For example, if you have a lot of random, spiky noise in the signal, that will show up as high frequencies. To clean it up, just do a Fourier transform, throw out any data with a frequency above a certain threshold, and then run an inverse Fourier transform on the remaining data to get back a smoother version of the original signal. This is called a low-pass filter, and it's more or less equivalent to taking a moving average of the original signal.
Where it gets really fun is that you can extend this, in a pretty straightforward way, to higher dimensions. A two-dimensional signal, where both the x- and y-axes are space, is just an image. JPEG compression is based on this concept: it removes the high-frequency signal in the image in order to store the data in a more compact form, at the expense of losing some fine detail (or creating those ring-like artifacts, if you throw out too much data). Add a third dimension for time, and now you have video. And so on.
The nice thing about all this is that it's very visual, so you can get a good intuition for it without having to know all the math inside and out. Here's a good page with lots of visualizations and interactive examples: https://www.jezzamon.com/fourier/index.html
The simple explanation: Lets say you have a one-dimensional time-domain signal, e.g. an audio signal measured by a microphone, which measures the displacement of air vs. time at a fixed point (assuming you dont move the microphone I guess)
The Fourier transform (of which the FFT is a discrete version of) decomposes that 1D time-domain signal (e.g. an audio signal, time vs. displacement) into frequency vs. magnitude and phase components
The frequency is basically the pitch. So for a pure sine wave, or pure tone - which sounds like those "off air" TV signals we used to get late at night back in the day. You get a bunch of zeros and a single "spike" at the frequency of the tone. The larger the amplitude of the signal, the larger the magnitude of the spike will be. As the pitch (frequency) increases/decreases, the location of this spike moves up/down along horizontal axis
The phase is basically the time offset of the signal. A tone which was delayed somehow will show up as a different phase. Note this is a relative measure - not absolute. So you won't be able to tell if the signal was offset by 1s or 2s, etc. because it has units of radians(angle), which have to "reset" as the angle wraps around the circle.
So for one signal (time vs. amplitude), you actually get two pieces of information (frequency vs. magnitude/phase)
However if you understand imaginary numbers/complex variables, those two signals are really just the magnitude and argument of FFT output, which produces a complex function
As someone who is absolutely terrible at math, I envy the people who grasp or at least can learn this type of stuff and get an engineering degree and license.
All I really know about FFT is that is changes a signal, its somehow used in processing signals of some kind, and it apparently from what I heard was the key to detecting nuclear detonations back in the day.