"of, pertaining to, or cause by the tides or a tide," 1807, a hybrid formation from tide (n.) + Latin-derived suffix -al (1). Also generally, "characterized by periodical rise and fall or ebb and flow."
A tidal wave (1819) properly is high water caused by movements of the tides; its use for "great ocean inundation caused by an earthquake, etc." is recorded by 1868. This now tends to be called a tsunami. Figuratively, "widespread manifestation of strong feeling," by 1870.