The iPhone's screen is bright, vibrant, and stunningly sharp. (It's got 320 by 480 pixels, crammed so tightly that there are 160 of them per inch, which is nearly twice the resolution of a computer screen.) 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 horizontal letterbox bars above and below the picture.
Some people are fine with that. After all, HDTV sets have the same problem; people are used to it. 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?
Fortunately, the iPhone gives you a choice. If you double-tap the video as it plays, you zoom in, magnifying the image so it fills the entire screen. Or, if the playback controls are visible, you can also tap 
or 
.
Of course, now, you're not seeing the entire original composition. You lose the top and bottom of TV scenes, or the left and right edges of movie scenes.
Fortunately, 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.
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