This is a very schematic sketch showing the origin of the delay observed between the the continuum and the emission lines in Active Galactic Nuclei (adapted from Alloin, 1990).
When an outburst occurs in the central ionizing source at time T=0, within a layer of matter at a distance R, the surrounding clouds respond to it and emit a line progressively received at Earth (first ray "a", then ray "b", and finally ray "c"). In principle we should see the line response delayed with respect to the continuum a time T = R/c. If the ionized line is stratified, lines with different ionization potentials will arrive at different times.