These certificates were issued to people who participated in US nuclear weapon testing at the Nevada and Pacific test sites.
Operation Ivy involved two tests. The first, Mike, was the first successful full-scale test of a multi-megaton thermonuclear weapon (“hydrogen bomb”). It was detonated on Elugelab Island yielding 10.4 megatons, almost 500 times the yield of the bomb dropped on Nagasaki. Eight megatons of the yield was from fast fission of the uranium tamper, creating massive amounts of radioactive fallout. The detonation left an underwater crater 6,240 ft (1.9 km) wide and 164 ft (50 m) deep where Elugelab Island had been.
Operation Plumbbob was a series of nuclear tests conducted in 1957, at the Nevada Test Site. It was the biggest, longest, and most controversial test series in the continental United States. It involved 27 explosions, some of which were in the atmosphere or on the surface. Plumbbob released 58,300 kilocuries (2.16 EBq) of radioiodine (I-131) into the atmosphere. This produced total civilian radiation exposures amounting to 120 million person-rads of thyroid tissue exposure (about 32% of all exposure due to continental nuclear tests). Statistically speaking, this level of exposure would be expected to eventually cause between 11,000 and 212,000 excess cases of thyroid cancer, leading to between 1,000 and 20,000 deaths. In addition to civilian exposure, troop exercises conducted near the ground near shot Smoky exposed over three thousand servicemen to relatively high levels of radiation. A survey of these servicemen in 1980 found significantly elevated rates of leukemia: ten cases, instead of the baseline expected four.
You can read more about the health consequences of surface testing at the Nevada site in this post.
Dido Queen was a 1973 20kt underground test.
Ming Blade was a 1974 underground test. The device had a yield of 20kt.