Weather
Weather is the state of the atmosphere at a specific place and time, described by temperature, humidity, precipitation, wind, cloud cover, and pressure.
Definition
Weather is what the atmosphere is doing at a particular place and time, described by temperature, air pressure, humidity, wind, cloud cover, and precipitation, and it is driven by the Sun heating Earth's surface unevenly, which creates pressure differences, wind, and moving air masses. In the mid-latitudes, much of the changeable weather comes from fronts where air masses meet, organized on a larger scale by baroclinic instability, which converts the temperature contrast between equator and poles into the cyclones and anticyclones steered by the jet stream. Numerical weather prediction solves the governing fluid dynamics and thermodynamics equations on a global grid using data from satellites, radiosondes, and surface stations, but because the atmosphere is chaotic, tiny errors in starting conditions grow until forecasts lose skill after about two weeks.
Example
A forecast calling for Charlotte to reach $85$ degrees and sunny with evening thunderstorms is a weather report, and a cold front passing through the Piedmont typically brings a line of thunderstorms followed by clearing skies, falling temperatures, and a shift of wind to the northwest. A $500$ hPa trough digging into the southeastern United States, combined with Gulf moisture and a surface low, is the kind of setup that produces the cold-season severe weather North Carolina sees, and Doppler radar can detect a developing tornado minutes before it touches down.
Key Insight
Weather is what you get today; climate is what you expect over many years, so weather is the mood and climate is the personality. Forecasts are limited to about ten days not because computers are too slow but because the atmosphere is a heat engine constantly moving energy from the warm tropics to the cold poles, and every storm, front, and jet stream is part of that transport, with its chaotic sensitivity to starting conditions setting a hard ceiling on how far ahead anyone can predict it.