Playing the MP4 video in question through Safari appears to have no effect at first, but gradually the operating system slows down before it freezes completely, after which only a hard reset will bring the device back to life. YouTube channel EverythingApplePro has posted a demonstration (i.e. not the original video) showing the exploit in action.
The bug appears to affect iOS builds as far back as iOS 5, while iPhones running iOS 10.2 beta 3 are said to power off and show the spinning wheel indefinitely.
If you fall victim to the prank, you'll need to hard reboot to get your device working again. According to a Reddit post by user Riddle, currently the top level domains hosting the video appear to be vk.com and testtrial.site90.net, but bear in mind that the video could be hosted on other sites quite easily and that URL shorteners can mask the actual address you're being linked to.
This kind of prank isn't new. Three years ago, a text exploit made the rounds that caused both Mac and iOS devices to crash.