Tape echo is an old form of delay, in which the signal is apssed through a line of magnetic tape to be repeated at a selected time. Digital delay has pretty much replaced tape echo, thoughsome people like the sound of tape echo better, and like the analogue nature of it. You can also play around with the tape, which is where flanging comes from. If you want to find genuine tape echo, rather than a digital efect attempting to simulate it, you probably need to look around for something second hand, but as I am quite happy with my Boss DD5, I haven't looked.
"Dozens of people spontaneously combust each year, it's just not that widely reported".