Double-tapping is actually pretty rare on the iPhone. It’s not like the Mac or Windows, where double-clicking the mouse means "open". On the iPhone, you open something with one tap.
A double tap, therefore, is reserved for three functions:
In Photos, Google Maps, and Safari (the Web browser), double-tapping zooms in on whatever you tap, magnifying it by a factor of two.
In the same programs, as well as Mail, double-tapping means, "restore to original size" after you’ve zoomed in. (Weirdly, in Google Maps, you use a different gesture to zoom out: tap once with two fingers. That gesture appears nowhere else on the iPhone.)
When you’re watching a video, double-tapping eliminates or restores letterbox bars.
See, the iPhone’s screen is bright, vibrant, and stunningly sharp. It’s not, however, the right shape for videos.
Standard TV shows are squarish, not rectangular. So when you watch TV shows, you get black letterbox columns on either side of the picture.
Movies have the opposite problem. They’re too wide for the iPhone screen. So when you watch movies, you wind up with letterbox bars above and below the picture.
Some people are fine with that. At least when letterbox bars are onscreen, you know you’re seeing the complete composition of the scene the director intended.
Other people can’t stand letterbox bars. You’re already watching on a pretty small screen; why sacrifice some of that precious area to black bars?
That’s why the iPhone gives you a choice. If you double-tap the video as it plays, you zoom in, magnifying the image so that it fills the entire screen.
Part of the image is now off the screen; now you’re not seeing the entire composition originally broadcast. You lose the top and bottom of TV scenes, or the left and right edges of movie scenes.
If this effect winds up chopping off something important - some text on the screen, for example - restoring the original letterbox view is just another double-tap away.