"fantastic series or medley of illusive or terrifying figures or images," 1802, the name of a magic lantern exhibition brought to London in 1802 by Parisian showman Paul de Philipstal. The name is an alteration of French phantasmagorie, which is said to have been coined 1801 by French dramatist Louis-Sébastien Mercier as though to mean "crowd of phantoms," from Greek phantasma "image, phantom, apparition" (from PIE root *bha- (1) "to shine").
The second element appears to be a French form of Greek agora "assembly. "But the inventor of the word prob. only wanted a mouth-filling and startling term, and may have fixed on -agoria without any reference to the Greek lexicon" [OED]. The transferred meaning "shifting scene of many elements" is attested from 1822. Related: Phantasmagorical.
In Philipstal's 'phantasmagoria' the figures were made rapidly to increase and decrease in size, to advance and retreat, dissolve, vanish, and pass into each other, in a manner then considered marvellous. [OED]