Meteorology is the scientific study of the atmosphere that focuses on weather processes and forecasting. Meteorological phenomena are observable weather events which illuminate and are explained by the science of meteorology. Those events are bound by the variables that exist in Earth's atmosphere. They are temperature, pressure, water vapor, and the gradients and interactions of each variable, and how they change in time. The majority of Earth's observed weather is located in the troposphere.
Climate is the average and variations of weather in a region over long periods of time. The climate of a location is affected by its latitude, terrain, persistent ice or snow cover, as well as nearby oceans and their currents. Climates can be classified using parameters such as temperature and rainfall to define specific climate types. Paleoclimatology is the study and description of ancient climates using information from both non-biotic factors such as sediments found in lake beds and ice cores, and biotic factors such as tree rings and coral, and can be used to extend back the temperature or rainfall information for particular locations to a time before various weather instruments were used to monitor weather conditions. Climate models are mathematical models of past, present and future climates and can be used to describe the likely patterns of future changes.
Meteorology, climatology, atmospheric physics, and atmospheric chemistry are sub-disciplines of the atmospheric sciences. Meteorology and hydrology comprise the interdiscplinary field of hydrometeorology. (You can learn more about meteorology from the Wikipedia article.)