One of the many common effect used primarily in music is called a delay. It might help if you call it an echo, because what a delay does is create a copy of part or all of a piece of audio and then repeat it just after the original. It "delays" the repeat by some set amount, usually a fraction of a second.
Now you can attach this effect to an entire vocal track, or you can just treat a single word or phrase in the track. The latter is called a "delay throw."
So how that would sound is that the audio - let's say a vocal - would be merrily singing along with no echo (delay). But then at some specific point in the song, maybe right before a chorus to build up anticipation or some other emotional effect, you decide to apply the delay effect to just one word or a short 2-3 word phrase.
In the following video by Dezz Asante, he shows you how to do this using Cubase recording software. Of course you can do the same thing in other DAW (digital audio workstation) programs. In Reaper there a several ways to do it.
You can use an effect buss and an automation envelope line like Dezz does in the video. But in Reaper I would be more likely to slice out the audio I want (Shift-Ctrl-S) to create a new audio item, and then simply insert the delay effect onto the new item.
See the aforementioned video below: