A simple answer to this question is “climate is what you expect, weather is what you get.”^[1]

Both weather and climate refer to local conditions (temperature, rainfall, wind strength, etc.) in a particular location or region, but the main difference between them is a matter of time. “Weather” refers to local conditions on the scale of minutes, hours, days, and even months to years: you can have a particularly wet month, warm winter, or rainy decade.^[2,3] “Climate” is an average of weather conditions over 30 years or more, and can be assessed for a single location, large area, or globally.^[2,3] While weather can change dramatically in a single location from day to day (for example, cold and rainy one day, followed by  hot, dry conditions the next day), climate generally changes less quickly because it represents the average of weather conditions over a longer period of time.^[1,2,3]

In the United States, weather has been measured directly by people for over 140 years^[1], meaning that sufficiently long records exist to also track modern climate in detail over the same time period. To track both weather and modern climate, geoscientists measure temperature over land and in the ocean, air pressure, humidity, rainfall and snowfall, wind speed, sunshine, and many other factors.^[4] Additional helpful information to track climate can include the frequency of record-breaking temperatures or rainfall events, the length of growing seasons, size of Arctic and Antarctic sea ice, trends in monthly weather averages over several decades, and many other aspects of the Earth system. Geoscientists also estimate past climate during times before direct weather measurements by analyzing data from tree rings, coral reefs, ice cores, and many other parts of the geologic record.^[4,5,6]

The reason that climate is usually measured by averaging weather conditions over 30 years or more is because many things can influence weather conditions on shorter timescales. ^[7,8] There are regular patterns in atmospheric and ocean conditions at annual to decadal scales that can lead to particularly hot, cold, wet, or dry years – or even wet or dry decades – all over the globe but which do not necessarily mean that the overall climate is changing.^[9] For example, when El Niño conditions are established in the tropical Pacific Ocean, the southern United States tends to be wetter, whereas the southern United States is dryer under La Nina conditions. In order to understand potential changes in climate, geoscientists need to measure and account for weather patterns like these over periods of several decades.

References

¹ What’s the difference between climate and weather? National Oceanographic and Atmospheric Administration
² What’s the difference between weather and climate? National Aeronautics and Space Administration
³ Climate vs. Weather National Snow & Ice Data Center
⁴ How do we observe today's climate? National Oceanographic and Atmospheric Administration
⁵ Past Climate Primer National Oceanographic and Atmospheric Administration
⁶ Paleoclimatology Data National Centers for Environmental Information
⁷ Understanding Climate National Academy of Sciences
⁸ Teleconnection Introduction National Weather Service
⁹ Teleconnections National Centers for Environmental Information

Learn more:

• Climate vs. Weather (Video) National Academy of Sciences
  Short video explaining the difference between climate (trend) and weather (variation)
   
• How do weather observations become climate data? (Webpage) National Oceanic and Atmospheric Administration
  Webpage explaining how weather data are collected and processed to become climate data products
   
• U.S. Statistical Weather and Climate Information (Website) National Centers for Environmental Information
  Website providing a large amount of downloadable historical weather and climate information, which may also be plotted by users on graphs and maps
   
• National Climate Assessment (Website) U.S. Global Change Research Program
  Website of the latest National Climate Assessment report, which summarizes the recent and future status of climate in the United States
   
• Present Day Climate Change (Factsheet), American Geosciences Institute
  Factsheet summarizing how Earth's climate is monitored, influences on the climate, and evidence for present-day climate change.