Youtube videos are not always meant to be watched. Yes, it may sound like an odd statement but its true. How many times have you left Youtube run in background tab and carried on working in the other tabs or different document? In fact, that is exactly what I am doing right now. No doubt Youtube is the largest media hub for multimedia content consumption especially if free stuff is your thing. So, when it comes to mobile, it is a major annoyance where you cannot play Youtube videos in background and carry on working on other stuff.
However, a minor bug on iOS 7 allows you to do this. We aint sure till when will Apple allow this to carry on how it is, but till then you are free to enjoy videos in the background. To do this, simply open, Safari or Chrome on your iPhone or iPad and go to the Youtube website. Play the video that you wish to play in the background and simply press the home button and come out. You will notice that the audio will stop on to play in the background.
Here is the trick now, simply pull out control center from the bottom and press the play button. Audio will start playing of the video you had on Youtube immediately. You can now carry on and do whatever you were as audio plays along in background.