Why Vestigial sideband (VSB) is amplitude modulation in which one sideband is sent complete and only a small remnant, the "vestige," of the other is left in place. Analog fast-scan TV used it because a full double-sideband video signal would need roughly 8 MHz, while filtering away most of one sideband squeezes the channel down to 6 MHz. The vestige is kept rather than removing the sideband entirely so the very low video frequencies and the carrier survive for simple envelope detection at the receiver.
Watch out The narrow-band FM description is wrong on two counts: VSB is an amplitude modulation scheme, not FM, and the filtering is done on the modulated RF, not on the audio beforehand.
Vestigial = vestige = leftover stub. One full sideband plus a stub, which is how analog TV fits video into 6 MHz.