You know how a butterfly lives an entire life in much less time than a dog does and a dog lives from being a puppy to being old in much less time than humans do and humans are born, grow and die much quicker than trees do.
Weather changes can be felt from day to day, month to month, season to season.
Illustration from: http://www.ruf.rice.edu/~leeman/GeoTimeSpiral.gif
Climate is like weather and it changes too, but its changes are not so apparant to us because these changes happen over geologic time, that is, in terms of the earth's growing, which is much, much, much, much, much slower than ours.
The history of our planet is marked by cold periods and warm periods that are surprisingly regular. Some scientists suggest that human civilization has arrived and thrived in what is no more than a brief warm spell in Earth's history.
Seen on a geologic scale, then, climate is just as unstable as weather.