Weather is the mix of events that happen daily in our atmosphere. Localized conditions (humidity, wind, temperature, etc) affect the atmosphere to create different weather conditions in individual locations around the globe. Weather is the short-term effects on the atmosphere.
Climate is the long-term trends in weather. Scientist average weather over 30 year periods to determine the climate trends for a location or region. Climate looks across all seasons and helps you predict what the weather will be like during different times of the year.
A simple way to think about it is: weather tells you what kind of clothes to wear today and climate tells you what kinds of clothes to have in your closet.