This is a good distinction to know when you're discussing or learning about global warming.
Weather: Weather is what happens over a relatively short period of time, like hours or days. Weather could be a thunderstorm or a blizzard or a sunny day. In general, don't use weather as evidence of climate change, such as "The earth must be getting warmer; we just had a 60 degree day in December!" That's not proof.
Climate: Climate is the statistical average of weather over a period of time. For example, the National Weather Service uses 30 years "normals" to measure climate. Climate determines what crops grow in a specific region and when they're planted and harvested. It is the weather pattern over months, seasons, decades, centuries. Those are trends scientists look at when studying global warming.