Among YouTube Red's benefits is the ability to play audio in the background while you go about your business using other apps or just sticking your phone back in your pocket. If you use headphones with their own play/pause button, then you can enjoy background-play ability on an iPhone without plunking down for YouTube's paid service.
First of all, you will need a pair of headphone like Apple's EarPods that feature an inline remote in order to pull off this free YouTube background play magic.
Secondly, you will need to use Safari instead of the YouTube app.
Here's how it works: Open YouTube.com in Safari. Next, play a video and then hit the Home button to close Safari. The video will stop but if you hit the play button on your headphones, the video will start playing again. (You might experience a few seconds of delay before the video resumes.) With the video playing in the background, you can use other apps or lock your phone.
Because the only headphones I have with an inline remote are the EarPods that came with my iPhone 6S, I didn't test this trick with any other headphones. I would wager, however, that it would work with other headphones as long as they have an inline remote to resume playing a YouTube video with Safari closed.
(Via Tech Insider on YouTube.)