It was vitally important to aid navigation so an accurate position of ships could be determined. Historic Maritime Greenwich is the centre of time because King Charles II established the first Royal Observatory in the Royal Park at Greenwich in 1675. It was founded to improve naval navigation, at a time when Britain was a strong sea power.
The first Astronomer Royal, appointed by the king, was Sir John Flamstead. His mission was to revise and improve the celestial tables and maps, in order to 'find out the much desired longitude of places, for perfecting the art of navigation'. In a period of intense exploration of the world, in search of new and safe routes at sea, the quest for longitude became paramount.
Royal Museums Greenwich has an excellent online article about the importance of this quest.
In 1715 the British parliament passed the Longitude Act, following a naval disaster (in 1707) that had brought to the fore once again the need of accuracy in calculating a ship's position.
The Act led to the establishment of the Longitude Board and of financial rewards for anyone who could solve the problem of calculating longitude at sea.
Those were the circumstances under which the English clockmaker John Harrison invented the marine chronometer, or sea-clock. Four of his timekeepers are exhibited in the Time and Longitude gallery of Royal Greenwich Observatory.
The US Naval Observatory (USNO) was established in Washington, DC, in 1830 to co-operate with the Royal Greenwich Observatory to develop accurate time-keeping for the navy.