There are two main uses that delay as an effect is used for, and generally, two different units for generating each.

Firstly, delay is used for time-aligning speaker systems. In these units, the input signal is simply delayed by a variable, usually milli or microsecond amount, so that a co-herent and clear sound is delivered to the listener from several different loudpeakers. These units may have several outputs or taps, so that the same input signal is delayed for different positions in an auditorium. The KT716 is an example of a 1-in 3-out delay line of this type. See the Q&A re the Haas effect for further discussion on this topic.

Secondly, delay is also used as an artistic effect, such as in echos. Delay, rather than reverb, is often used on vocals to thicken the sound. Unlike reverb, a delay effect tends to leave the vocal clearer in the mix, especially if the mix is quite full. Again, in todays units, the control can be quite sophisticated, but you will generally be able to alter the number of delays (or taps), how quickly they occur, and how much each delay decreases (or occasionally increases) in level, and thus the time the delay sound takes to fall away.