According to the theory of plate tectonics, tectonic plates bearing the world's continents slowly move relative to each other, rearranging them in noticeable ways only over timescales of millions of years. Tectonic plates move about as fast as your fingernails grow. They get pushed around by a phenomenon called seafloor spreading, where the margins of oceanic plates are constantly being subsumed into the mantle, allowing new magma to rush up to fill the cracks forming at the plate's center. Crevices caused by seafloor spreading extend in one continuous line around the ocean floors of the world.
The placement of the continents affects global climate in several ways. The relative arrangement of the continents may regulate the coming and going of major Ice Ages more than solar cycles or any other factor. When there is a continent around the northern or southern polar regions, it is at risk for becoming glaciated and impacting global climate. Especially in the case of Antarctica, which is exclusively polar, a frigid circumpolar current begins circulating the continent and causing feedback cycles of cooling and glaciation. As a result, the Antarctic interior is the largest desert in the world; desert is defined as the absence of moisture. Extremely low temperatures lock all moisture up in ice.
Once, tens of millions of years ago, Antarctica was a lush forest continent. Throughout most of the planet's history, forests extended from pole to pole. Dinosaur fossils have been found within 20 degrees paleolatitude of the South Pole. This is especially remarkable considering that dinosaurs had a slower metabolism than mammals and probably didn't deal with the cold as well. Their sensitivity to global climate is probably what contributed to their downfall. Their inability to deal with global climate changes are what led mammals to survive the mass extinction and for dinosaurs (except the ancestors of birds) to die out.
Another factor that strongly influences global climate is whether the continents are pushed up against each other, as in the supercontinent Pangaea, or largely apart, as is the case today. When the continents are together, it means that much of their land area is very far from the oceans, making it difficult for moisture to reach them, producing deserts. It is thought that the largest desert that ever existed was the center of the continent Pangaea. Today, life is abundant in the interior of most continents, but back then, Pangaea's center would have been devoid of practically all life.