tape delay is/was a technique of creating a delay effect using tape heads and tape. here's the basics:
i'll use guitar as an example.
guitar signal goes into delay box and is routed to a tape head which records the signal to a moving reel of tape. The signal then goes to another tape head that plays the signal back.
The time it takes for the piece of tape to move from the first head to the next one that plays it is what creates the delay.
The delay time can be changed by changing the distance between the heads.
This was originally done with analog reel to reel machines, but the box you are talking about is probably a really really long continuous reel. Once it gets to the end of the reel, it loops it back to the part of the reel you started with, and if it doesn't have an erase head, you'll hear the signal from when you started, hense the "hours of fun". At one point it repeats itself and you'll have to erase the reel.
tape delay is known for a mellower warm delay with less high end than a digital box.
hope that makes sense.
