A Fourier transform decomposes a signal into the frequencies that make it up. Think of it like this: if you hear a chord on a piano, a Fourier transform tells you which individual notes are being played and how loud each one is. Any signal that varies over time — a sound wave, a stock price, a heartbeat — can be represented as a sum of sine waves at different frequencies. The Fourier transform finds those frequencies and their amplitudes. The result is a frequency spectrum: a chart showing "how much of each frequency is present in this signal." Why this matters outside of math: JPEG compression works by taking the Fourier transform of image blocks and throwing away the high-frequency components (fine detail) that your eye is less sensitive to. MP3 compression does the same thing with audio. When your doctor reads an MRI, the raw data is in frequency space — the image is reconstructed via an inverse Fourier transform. The core insight is that time-domain and frequency-domain are two equivalent ways to describe the same signal. You lose nothing by switching between them. You just see different things.