Geography is a descriptive study. Geographical distinctions are applied to land masses or bodies of water, and the boundaries between them are not able to be clearly defined. For example, we speak of mountains, rivers, plains, lakes, seas, oceans etc. So, the question remains "where does the mountain begin and the flat land end?" The polar regions, usually considred cold and barren, are the result of the combination of the rotation of the earth and the amount of sunlight that reaches the area. If the earth was stationary there would be no axis of rotation and therefore no "polar" region.
This answer seems to suggest that the polar regions are not clearly defined, which is misleading. In fact, the polar regions are defined as the areas north of 60°N latitude and south of 60°S latitude.
- The Arctic region encompasses the area north of 60°N latitude.
- The Antarctic region encompasses the area south of 60°S latitude.
Additionally, the polar regions are not "cold and barren," as you wrote in your response. Sure, the Antarctic region meets this criteria as there is no native population and very little in the way of plant and animal life. However the Arctic region is teeming with life - a wide variety of plant species and numerous animals species (including bears and musk oxen), all live in the Arctic region and support the native human population.
As for the geographical processes that shaped the poles, the most influential factor affecting Earth's latitudes is the angle of incidence of the sun's rays. At the equator, the sun hits the Earth head on and the amount of solar energy absorbed by the ground is highly concentrated. In contrast, the sunlight hits the poles and disperses over a larger area of land, so the solar energy is less concentrated. This means that the polar regions receive less solar energy as compared to the equatorial and mid-latitudes. Another important factor is in the albedo effect, which is the reflectivity of Earth's surface. (The albedo effect is an example of a feedback loop.) In equatorial regions, the dark rainforests serve to "soak up" solar energy - these areas have low albedo, or reflectivity. On the other hand, polar regions are icy and very reflective - they have high albedo. The highly reflective nature of ice reflects the little solar energy that hits the polar regions away from the planet, meaning the region stays cold.