YouTube introduced transcription on its desktop website some time ago and it proved to be particularly useful in long videos. It helps you find a certain commend or extract your favorite quote by searching the automatically generated transcript of the video.
Screenshots of the transcript feature
As of now, some users report the new feature being implemented in the native Android app. There’s a dedicated “Show Transcript” button below the video’s description. The transcript itself is quite similar to its desktop version, it’s just adapted to the mobile’s UI.
As most of Google apps’ updates, this one also seems to be server-sided so you might have to wait until it becomes available to you too.