We have so many exotic plug-ins these days that the simpler ones tend to get ignored. And you can't get much simpler than delay. Take a signal, delay it in time, lower it in level, and add it back to the original. Suddenly everything is just that little bit more sparkly. You can even feed the delay back into itself and get a repeating, decaying echo. In the 'good old days' of audio this was sometimes called spin echo.
In those 'good old days', delay was created using a spare stereo tape recorder, often a Revox A77 or B77. You can record and play back at the same time, but there is a delay created by the distance between the record and playback heads. You could get as many different delay times as the tape recorder had speeds, often just two. Or if the tape recorder had a variable speed facility, you could get a wider range, which was simply set by ear.
Delay times these days can be set by ear, but you won't be able to resist looking at the milliseconds display. Or you can often just tap the tempo. Both methods are good. Or you can, if you wish, calculate the delay time. Here's how to do it...
First start with the magic number, 60,000.
Next, divide the tempo of the song in beats per minute into 60,000. So if the song runs at 120 BPM, the result will be 500.
So you can set a delay time of 500 milliseconds, and the delays will correspond exactly to whole beats.
But often this doesn't sound too good as the delay gets confused with the original signal. But if you divide 500 by 2, or 3 or 4, or maybe even 5, you will get a range of delay times that will give interesting effects that are related to the tempo. Dividing by three for example will give you 167 milliseconds, which will give you a delay that is in triplets.
Or multiply 167 (Actually 166.6666 recurring) by two to give 333 ms and you will have yet another tempo-related delay.
But where does the magic number of 60,000 come from? The answer is simply that it is the number of milliseconds in a second (1000) multiplied by the number of seconds in a minute (60). Of course, you don't have to set delay times like this, but it is an experiment that every musician/engineer should try out at least once in their career.