Reverberation and delay are two methods of signal processing that are often incorrectly equated. The confusion comes from the fact that they are so closely related.
Reverberation is multiple blended sound images created from reflection. A few common reverb effects are Reverb Room and Reverb Hall. Reverb Hall would be like playing guitar in a small school gym. The sounds of the guitar would bounce around the room, reflected off the walls and floor and ceiling and would thus build into a new sound.
Delay is also called echo, though I think that blurs the line. Delay is one or more distinct sound images.
Here is where reverb and delay are related. Stand in a huge room and yell "hello." The very first sound you hear reflected off the walls is an echo. That echo quickly turns into reverb as the sound is reflected off a second, third, and fourth surface.
Think of delay as a single copy of the sound at a later time.
Reverb is commonly added to a voice to fill it out. Using the reverb knob (also known as the talent knob), offending frequencies can be masked. Reverb can give a guitar a fuller sound.
Delay is used primarily in two areas; speaker placement and guitar effects.
When a sanctuary is so big that it requires speakers in more than one location from front to back, delay is used on speakers not in the front. This way, sounds from speakers in different depth locations reach the person's ear at the same time.
Delay can be used on a guitar for effects which permit the player to play less but sound like they are playing more.
Reverb and delay are terrific signal processing effects which can sculpt a sound to fit the need.