How can satellites be used for weather?
By taking pictures of weather phenomena.
We have 2 main types of satellites that take pictures of the Earth showing reflection of different wavelength.
The two types are Geosynchronous and Polar orbiting. Geosynchronous are at a high enough altitude that they orbit over the same point on the Earth all the time. Polar orbiting satellites are much lower and circle the globe every couple of hours.
The wavelengths we can look at are visible light which shows us sunlight reflecting off of cloud tops. Infrared shows us the temperature of the cloud tops. Near infrared is a combo of 80% visible light and 20 percent infrared. We can also analyze 6.7 microns which shows us water vapor, and not liquid water (clouds).
These pictures shows us where there is clouds and how developed the clouds are. In the case of the water vapor shot it can show us a very good picture of where the jet stream is. If we compare visible vs infrared we can tell where there is fog.
All of these things can be use for observing what is going on and forecasting what will happen.