Ovdersimplifiying, look at the clouds in the satellite photos, look at the wind direction and guess where the cluods will be tomorrow. (Yep, there are more difficult parts, like correcting this using the pressure, and when two wind currents colide, and there is the effect of the mountains or the sea, and...) So doing it by hand is very difficult and error prone, and weren't very accurate. Now the computers models are very accurate.

When we have an important outdoor activity, she takes a look at the computer models in pages similar to this and she gives a personalized forecast. For example, a long time ago we had the bithday party of my older daugther in a zoo. My mother said that it will be rainy early in the morning but we should not worry, becuse it fill be fine from 10am to 6pm, that includes all the time of the party. She was correct :).