Climate is NOT the same thing as weather. Instead, it is the aggregate of many factors of the interaction of land, water, air, and sunlight over many years. Climate drives the weather, but is bigger than weather alone.
Geologic record and astronomy clearly show large scale changes in Earth's climate happen naturally. Some of these changes are periodic, based on Earth's orbital parameters (such as the Milankovitch Cycle.) Other changes have to do with the particular set of circumstances of continental position, sea level, mountain building, vegetation, etc.
Changes happen on the scale of days and months (i.e., weather), years, centuries, millenia, millions of years, and more. The relative land-water ratio, the composition of the atmosphere, etc., are all subject to change.
Natural climate changes can still affect human societies and populations.
Human contribution to climate change comes largely from the release of greenhouse gases. The carbon in the carbon dioxide from buring coal and gasoline had been sequested away tens to hundreds of millions of years ago, when the carbon dioxide levels in the atmosphere were many times the present level. In such situations, the world was much hotter than today, and there were no continental glaciers and few alpine ones. The current meltback of glaciers around the world (many of which had survived the glacier-interglacial cycles of the Ice Ages) shows that the human-generated component of global warming is taking us outside of typical Ice Age cycles.
Studies of previous deglaciations show that freshwater flooding into the northern Atlantic can temporarily shut down the Oceanic Conveyor Belt which dominates modern oceanic circulation. This in turn disrupts global distribution of heat, causing massive climate changes. Past events of this nature have taken only 5-10 years to happen once initiated, resulting in a quick switch to a world with very different weather patterns.