Mike was impractical as a weapon. It used a liquid deuterium fusion fuel (deuterium is a heavy isotope of hydrogen) and consequently the whole apparatus had to be cryogenically cooled to not far above absolute zero. A whole gas liquefaction industry had to be founded in order to make this possible.
The U.S.A. had felt itself to be in a race with the USSR for a fusion weapon - not for reasons of national prestige, as in our Moon program, but as a deterrent against attack. The military had felt pretty good about its nuclear inventory, until in September, 1949, American "sniffer" planes picked up radioisotopes over the northern Pacific which had their origin (as measured by their proportions and their known half-lives) on the same day - meaning they were formed in the heart of a nuclear explosion. In fact, the American commercial company that developed the analytical techniques and had been working with routine samples for months was able to specify nearly the exact time of the explosion; they were only off by 1 hour, though the explosion had been a couple weeks before.
Suddenly, we no longer had a nuclear monopoly. And no one trusted Joe Stalin not to use, or at least, threaten to use, his new capability. American scientists decided we needed a hurry-up program to move up to a fusion bomb, which had been proven theoretically possible years before. They had been sitting on a proposed design, called "Alarm Clock" but it was still just a theoretical mathematical construct.
The big deal about hydrogen bombs, as opposed to atomic bombs, is that their yield is essentially unlimited; you just add more fuel to the design. (Fission, or atomic bombs, have inherent limits on yield to a few hundred kilotons.) Hydrogen bombs, however, require an atomic bomb to set them off. They must attain pressures and temperatures comparable to the interior of the sun in order to ignite the fusion reaction. (The sun, of course, is fusing hydrogen into helium all the time.)
The work was slowed but improved by the invention of the Ulam-Teller design (named after the physicists who came up with it). Instead of explosive compression of the deuterium, they would use the shock wave of the fierce radiation from the fission bomb to compress the fuel faster and better, leading to better ignition and yield.
The Ivy Mike shot was fired without a hitch. To help analyze the physical processes as they happened, engineers constructed "light pipes" into the side of the device and then led that light down a 9,000-foot plywood tunnel containing helium-filled polyethylene balloons to a fortified bunker on another island, where instruments would measure the light and neutron fluxes before the fireball vaporized the whole thing.
Ivy Mike yielded 10.4 megatons, meaning the explosion was equivalent to 10.4 million tons of TNT going off at once. It was 1,000 times the power of the bomb that destroyed Hiroshima.
The explosion left a crater 200 feet deep, erasing the island of Elugelab. Here is a Google Earth image of the site (which is the northernmost part of Enewetak in the first picture.) I've drawn a diameter which shows it to be almost a mile across. The crater to its right is from H-bomb test Castle Nectar a little over 6 months later (1.7 Mts).
The small fish-shaped island just to the east of that is Bogon, home to a small atomic weapon blast: Seminole (13.7 kilotons). You can see the difference in size of craters.