Nowadays, it has become a norm to use the terms of climate and weather synonymously, whereas there is a lot of the difference between the two as the following lines will explain.
Climate is the average weather of a place observed over a very long period of time, usually for thirty years or more. These conditions are well-established and well known at a particular location. For instance, it is known that the climate of London is mild both is summers and winters with frequent precipitation. What does it mean? It means that it is a well-established fact that the summers as well as the winters at London are USUALLY mild and London has got a rainy climate.
To cite another example, the climate of Cairo is hot and dry in summer and cool and dry in winters.. It means that the summers at Cairo are USUALLY quite hot while the winters are cool. The statement of weather is also giving us another information that climate is dry both in summer and winter and indeed it is! Cairo records only one inch of rainfall annually.
Weather is the CURRENT condition of temperature, pressure, relative humidity and rainfall at a particular place and it can deviate considerable from the long term average described above. It is a very easy to understand concept. During recent years, especially after the year 2000, there have been unprecedented heat waves occurring in London during summer. So if during a heat wave we experience hot temperatures, we would say that the weather of London is hot today at such and such date of July. It does not mean that the climate of London is hot in July.
Similarly for Cairo if, for instance, we experience an unusually cool summer in July and the temperature drops to a very pleasant range, we say that weather of Cairo is pleasant today at such and such date of July. It will not, at all, mean that the Climate of Cairo is pleasant in July. To explain further, if we, for any reason, observe a sudden downpour at Cairo of more than 5 inches in few hours then we would say that the WEATHER of Cairo is rainy today. It will have no effect on the CLIMATE of Cairo which is dry and it is a well-established fact.
It follows from above, then, that Climate is the average weather of a place observed over a very long period of time, usually for thirty years or more while weather is the current state of temperature observed at a certain place.