Back in the late 1950s and early 1960s, the American military had a dream. That dream was to create a nuclear rocket launcher, and with it, the world's smallest nuclear rocket. The M-28/29 "Davy Crockett," and this massively tiny explosion (at around 3:35, if the video doesn't load properly), was the result.
The miniature nuke came about from the desire to be able to use a nuclear weapon on a tactical, battlefield level, as opposed to only using strategic, city-destroying nukes.
Faced with the prospect of Soviet infantry and armor streaming through the Fulda Gap in Germany, NATO forces devised ways in which they could delay the Communist advance. Since this was one of the peaks of the Cold War, American war planners thought nothing of arming troops with a W54 nuclear warhead attached to a recoilless rifle. The resulting weapons system was known as the "Davy Crockett," and it's range was just one and a half to two and a half miles, depending on the configuration used.
Which meant that depending on the range it was fired at, plus other factors like the direction the wind was blowing in, it might've been a suicide weapon for its operators under the right conditions.
Through a weird quirk of physics, creating a small nuke is actually much more difficult than creating a large nuke. With a large nuke, you could essentially just keep adding additional fusion stages until you have something like the Soviet Tsar Bomba, but a small nuke requires precise assembly and difficult mathematics. The W54 eventually took a few tries, but it finally worked with some of the last American atmospheric nuclear tests, in the form of Little Feller I and II, part of Operation Sunbeam. Attorney General Robert F. Kennedy was in attendance.
The test seen up top had a yield equivalent of 18 tons of TNT, coming from a warhead that weighed only a little more than 50 pounds. Later, a variant of the warhead saw use in the Special Atomic Demolition Munition, also known as the "backpack nuke."
Luckily, we never got to see it in real action.