Here's where the bomb fallout comes in: Detonation of nuclear bombs during tests in the 50s and 60s produced "artificial" radiocarbon in the atmosphere. This is known as the bomb effect. The global carbon exchange cycle has thankfully been reducing the nuclear bomb-released radiocarbon, such that levels of bomb carbon were 100 percent above normal between 1963 and 1965, but about 20 percent above normal (i.e., pre-nuclear bomb testing) in the 1990s.
Video: What Would Happen If Sharks Disappeared?
The radiocarbon pulse in the environment therefore created, and continues to create, time stamps, so scientists can measure radiocarbon levels in something (in this case, the shark vertebrae) and pair those measurements with a reference chronology.
The technique has been used to better date trees, but in more recent years, it's been applied to sharks, which can be notoriously difficult to study. That's because many sharks have large ocean ranges, swim in deep water, grow up discreetly in "nurseries," and can be hard to tag-release-recapture.