Weather refers to the short-term conditions of the lower atmosphere, such as precipitation, temperature, humidity, wind direction, wind speed, and atmospheric pressure. It could be sunny, cloudy, rainy, foggy, cold, hot, windy, stormy, snowing … the list goes on.
While weather refers to short-term changes in the atmosphere, climate change (global warming) refers to atmospheric changes over longer periods of time, usually defined as 30 years or more. This is why it is possible to have an especially cold spell even though, on average, global temperatures are rising. The former is a weather event that takes place over the course of days, while the latter indicates an overall change in climate, which occurs over decades. In other words, the cold winter is a relatively small atmospheric perturbation within a much larger, long-term trend of warming.