Yeap that would be delay. If you want to get just certain words to trigger it (like at the end of a line like you were saying), you have to set up a seperate track with the delay effect on it. Then set up a send from the vocal track to the delay track. Automate the send on those words or whatever and ur in business.
Most delays link up to the project bpm and you can adjust the delay in 1/4, 1/8, etc. notes, so the delay is in time.