Meteorologists all over the world measure temperatures, wind and precipitation; cloud cover and air moisture at fixed times of the day every day throughout the year.
Based on long time series of such data at thousands of places around the world, it is possible to calculate the average weather at local places or regions over time.
The current normal used by many meteorologists is based on the average data from 1961 to 1990. In other words, the normal is the average weather over thirty years.
The normal can also be calculated over hundred years, but that is more unusual.
It is therefore possible to say what the normal temperature, wind and precipitation are e.g. 20 March in New York, Beijing, Oslo and thousands of other places. But bear in mind “the normal” temperature, wind, cloud cover and air moisture means the average weather this day and this place measured over decades, which means you can have a good guess at what weather to expect.
When consulting these normals, you can find out what kind of weather to expect if you travel to Cairo or Anchorage in March.
You will know that you are likely to get warm, dry and sunny weather in Egypt at that time, while if you go to Alaska, you should prepare for cold winds and maybe snow. These expectations are based on the normals – the average weather over a long time period, in other words; the climate.
You never know the weather, though. You might to your surprise get snow in Cairo and a warm and nice spring day in Anchorage.
The weather from one day to the next, or even from one year to the next can of course deviate quite a lot from the normal.
The weather one or even 3-4 years in a row does not influence much on the average weather over a thirty years period.
Oscillations like El Nino Southern Oscillation (ENSO) and North Atlantic Oscillation (NAO) typically have substantial effect on the weather, but usually little effect on the climate.
American climatologists often use the last three decades rather than the fixed 30-year periods.
What do we mean by Climate? (Met office)