When you talk about weather, you are really talking about the air. Weather is what the air is like in any one place at anyone time. How hot or cold is the air? How much dampness, or moisture, is in it? How fast is the air moving? How heavily does it press on the earth?
The Oxford Dictionary defines weather as the condition of atmosphere at a certain place and time, with reference to the presence or absence of sunshine, rain, wind, etc. The Sun is basically the 'engine' that fuels the world's weather. The equator which is the area on Earth which faces closest to the Sun is heated the most while the two poles receive the least heat. The atmosphere is constantly trying to even out the temperature irregularities by carrying warm air to places which are cold and cold air to places which are warm. But evening out all these irregularities are more complex than that. Other factors such as friction with the land and sea, rotation of the Earth and also air which is held within the confines of the atmosphere by the earth rarities. These cycles and forces create complex and ever changing patterns.
In short, weather is the way water changes in the air. Without water, there would be no clouds, rain, snow, thunder, or fog. In fact, weather plays a big part in our lives and affects many of the things that we do and also affects all things on Earth.
Weather is different at different parts of the world. For example, in deserts, it very rarely rains. In tropical jungles, it is hot and steamy. Weather keeps changing all day.
On the other hand, climate stays much the same one year after another. Climate tells what the weather is like in general, all year round. For instance, tropical countries have hot climates and the Arctic has a cold climate.
However, scientists have found that some present deserts did have a more pleasant climate which is more conducive to plant life than present - the Sahara Desert is such. In other words, climatic changes have been taking place over a period of time and it would be a mistake to think that the present climate experienced would remain unto forever. Current discoveries like global warming and 'wintering' (ash caused by meteorites bombarding the earth's surface or volcanic activity which prevents the Sun's heat from reaching the Earth's surface) makes it easier to understand why some civilizations suddenly vanished.
A person who studies the weather, is known as a Meteorologist. Meteorologists study the weather by recording and analyzing data. You can become an amateur meteorologist by building your own weather station and keeping a record of your measurements. After a while, you'll notice the weather patterns that allow meteorologists to forecast the weather.