Yeah, that's not a vocal technique, it's an effect processor that the vocal part is being put through. The effect is usually called "delay" because a delayed copy of the original signal (or several delayed copies) is being created. When the copies get progressively quieter (which is the normal use) it sounds like an echo, but is usually louder, faster and contains more actual echoes than you find in most natural environments. Any sound can be put through a delay.
There are many ways to add delay to a signal: you can use a stomp box effects processor (which is quite common for guitar), you can add the effect live using a program like Ableton, or you can add it in the studio manually or via the effects processors in your DAW. It can be particularly difficult to add to a live vocal part because severe feedback can occur if the delay effect gets caught in the same microphone that is being delayed.
It's pretty difficult to find rock or pop music that doesn't use at least some delay. A classic rock example that makes particularly heavy use of it is Pink Floyd, for example on the albums Animals and Dark Side of the Moon (and honestly, pretty much every album they made).