You cannot tell with a single coin flip whether the coin is fair (50% probability of heads) or not. You cannot predict any particular flip of the coin. But if you flip a coin 1000 times and it comes up heads 659 times, you can say with a high degree of confidence that the coin is not fair. You still cannot predict any particular flip, but we can predict that we would see about 66 heads if we flipped the coin 100 times. If tomorrow we flip the coin 1000 times and it comes up head 831 times you have a high degree of confidence that the distribution of heads and tails changed since yesterday.
Weather is like a single coin flip. You cannot tell in advance easily whether it will rain or not or exactly what temperature it will be. But we can make statements about the average temperature in January or the average number of rainy days in April. If we see those values change over time, as we have all over the Earth, you can say that the climate is changing. With enough measurements over a long enough period of time, you can see the climate change at only one weather station. If we also see the same thing happen at thousands of other weather stations over decades, and we observe the ice sheets melting and the humidity increasing, then that's clear evidence of the climate changing.
That's the difference between weather and climate. Weather determines what you wear on a particular day. Climate determines what clothes you have in your closet.
Source: http://rss.slashdot.org/~r/Slashdot/slashdotScience/~3/pX1ZiX4AG_Y/story01.htm
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