It's a Copy>Paste Special>Transpose on a waveform, converting Rows/Columns that are time/amplitude (with wavelength embedded) into Rows/Columns that are frequency/amplitude (for a snapshot in time).
People love to go on about how brilliant it is and they're probably right but that's how I understand it.
Pretty much, but phase is also included. Which matters for some things.
But mostly not for ears it turns out!
Phase matters for some wideband signals, but most folks struggle to tell apart audio from hilbert-90-degree-shifted-audio
Phase is required if it is to be a reversible transform. Otherwise would just be a Functional.