Hillsong United uses the dotted 8th note delay alot, and I've incorporated this delay into many posts, without a proper explanation about how it works. I hope this post clears up all your queries.
Delay effects repeat the note or chord you played after a specified timing. Because the band's tempo may change, it is highly advisable that you key in the tempo using a tap tempo, which is a button on your delay pedal that allows you to tap the tempo in with your foot (or finger). I use the digital delay a lot because it does not colour the repeated note much.
I set my delay settings to: time = dotted 8th note (see picture on the right), feedback = 20%, mix = 47%. There's no hard and fast rule for this though, it depends alot on your playing style and personal preference.
While delays are often used to make a solo sound bigger, or to create an airy effect, setting the delay at this tempo repeats the note at regular intervals such that it sounds as if you're alternate picking rapidly, as demonstrated in 'the time has come' and 'an introduction'.
In the video above, I played palm mutes and single notes with the metronome, with and without delay. I then played 'an introduction' and 'take it all' with and without delay. The delay changes the feel of the guitar riff by constantly repeating the notes, making it sound as if I'm picking rapidly - I did not do any alternate picking here, but did leisurely downstrokes instead.
To get an idea of what's happening, refer to the following diagram:
The above represents one bar, or four beats (quarter notes). The picked notes (topmost row) come in on the beats 1 & 2 & 3 &... (the 8th notes) while the metronome ticks at 1, 2, 3, 4 (the quarter notes).
The delay notes come in 3/4 of a beat after the note is played - it appears right after the next note is played. For example, once the note is picked at '1', its delay comes in right between the notes played on '1&' and '2'. The delay causes the '*' notes to come in between the '^' notes, making it sound as if you are alternate picking.