Mike the signal chain that
Dave has suggested is simply a way of controlling how loud the delay effects are. The vocal side chain that is controlling the compressor which will I assume be placed after the delay effect will duck down the delays while the vocal line is actually present.
(How much the delay effect is ducked down depends on how the compressor is set up) As the delays are lower while the vocals are present they wont interfere as much or step on the vocal very much only hint in the background.
But as soon as the vocal stops the delay effects will jump up back to their normal return level and hence be louder. Only the last word or words will end up being heard.
(in the delay that is) This was discussed in another thread a while back. For this to work though the vocal needs to be on its own track and be assigned direct to the main outs. (or to a vocal buss) The vocal signal also needs to be sent in to the compressor which is after the delay effect also on its own buss. Vocals obviously also need to sent to the delay buss too.
This concept also applies equally well to reverb and people should go the extra mile to set this up because it can make quite a difference in terms of how much the reverb will cloud a vocal while the vocal is present. In fact you don't really want much reverb at all while the vocal line is actually present. It is after a word is sung or spoken and there is no more vocals after that point that the reverb can be brought up a notch and hence be heard. It creates the illusion there is more reverb on the vocals that what there actually is.
Another good trick for reverb too is to use a longer predelay and a shorter reverb time. That will also create the illusion the reverb is bigger than it actually is. If you combined that with sidechaining or ducking it ends up very convincing.