Delegates from 25 countries voted in Washington on October 13, 1884 to make the meridian through the Royal Observatory at Greenwich the zero line of the world's longitude, and Greenwich time the basis of the world's clocks. The vote was not unanimous. France abstained and went on using the Paris meridian for its own charts for decades, and it did not accept Greenwich time in ordinary use until 1911. The line has been the world's since. It stands.
The choice was decided by shipping before it was decided by diplomats. By the 1880s the British Admiralty charts and almanacs, which were drawn and calculated from Greenwich, were used by far more of the world's merchant fleet than anyone else's, roughly two thirds of it by one estimate, and a navigator who wanted to fix his longitude looked it up in a British table. The conference in Washington, called by the president at the request of the American railroad and survey people, was there to ratify what the sea had already settled.
The question of time was harder. The delegates agreed that the day should begin at midnight and that the world should be divided into zones. The zones took years. The railroads, which had already worked out their own regional times, were the first to take them up. The conference also declined, on a French proposal, to rule out neutral names for the line and the time, and the names Greenwich meridian and Greenwich mean time have stayed in place.
Greenwich itself is the reason the line matters now. The observatory was moved out of London in the 1950s, but the brass strip marking the meridian still runs through the old courtyard, and visitors stand on it with one foot in each hemisphere, and the clocks of the world, including the ones set by satellite, still count from the line the delegates picked in Washington in 1884.