The development of the telegraph in 1835 made weather forecasting possible. Before that time, people used various methods to guess changes in the weather. Some observations were accurate. For example, the correlation of barometric pressure to weather changes. However, there was not enough geographically widespread data to methodically forecast weather.
The Britsh government charged Francis Beaufort and his student, Robert FitzRoy with collecting weather information then disseminating it to ship captains. Their office eventually morphed into the British Meteorological Office.
An especially destructive 1859 storm inspired FitzRoy to develop meteorological charts and coin the term “forecasting the weather.” Fifteen stations telegraphed weather data to their office. Early methods were not as effective as they are now but were a vast improvement over nothing.
The scope of weather stations expanded and FitzRoy especially helped build the modern science of meteorology.
By 1861 The Times published regular weather forecasts. In 1911, soon after the invention of voice over the radio, forecasts were broadcast to ships.
Weather forecasts were especially useful during wartime when deciding when to sail ships and fly planes.
Today, weather forecasts are a part of daily life. There is even a full-time weather forecasting channel. Radar, satellites, and weather balloons send enormous amounts of information used to make ever more accurate predictions.