In the 18th century, the only way to navigate accurately at sea was to follow a coastline all the way, which would not get you from Europe to the West Indies or the Americas. Observing the sun or stars would give you the latitude, but not the longitude unless done in conjunction with a clock that would keep time accurately at sea, and no such clock existed. After one too many maritime disasters due to navigational errors, the British Parliament set up a substantial prize for a way to find the longitude at sea. The film's main story is that of craftsman John Harrison: he built a clock that would do the job, what we would now call a marine chronometer. But the Board of Longitude was biased against this approach and claiming the prize was no simple matter. Told in parallel is the 20th century story of Rupert Gould, for whom the restoration of Harrison's clocks to working order became first a hobby, then an obsession that threatened to wreck his life.
