In her announcement post, YouTube Software Engineer Pallavi Powale said they had to overcome some engineering hurdles to make the update happen. They had to make sure that the app can change the duration of the audio without affecting its quality. As you know, playing videos faster could make voices sound like chipmunks, while playing them at a slower speed could lower the pitch. The team had to do the same thing for the desktop version, but the problem with mobile is that phones are subject to hardware and network limitations. That's why when you change the playback speed on your phone, YouTube adjusts the video quality "to be only as high as [the app] can download dependably."
The feature is already live for a lot of people -- to try it out, simply tap on the hamburger menu at the top of the app's interface. After that, choose "Playback Speed" from the menu that pops up and choose the speed you prefer.