What it is
The vocal tract — the tube from larynx to lips — is an acoustic resonator that amplifies certain frequency bands; these amplified peaks are the formants. F1 is the lowest of them, governed mainly by overall tract length and mouth opening: a wider opening or a shorter tract pushes F1 up; narrowing or lengthening pulls it down.
It does not change with volume — only with the shape of the tract.
Where it comes from
Read it off the spectral envelope: draw the smooth outline over the harmonic series, and the position of the first hump is F1.
On the spectrogram it is the lowest steady energy ridge. SonaLab marks it in real time in Resonance Depth Detection and the Formant Tracker.
How to read it
A low F1 (roughly <400 Hz) usually corresponds to deep resonance, a low larynx and a relaxed, spacious tract; a high F1 corresponds to a shallow, flat, squeezed tract.
Vowel identity is decided by the F1/F2 combination (“ah” has a high F1, “ee” a low F1).