Understanding the role of solar radiation in the Earth's climate system can help us grasp important concepts such as:

The causes of the seasons:
Seasons are caused by the tilt of Earth's axis. The tilted axis means that the northern and southern parts of Earth do not receive equal amounts of solar radiation (energy per unit area). When the southern hemisphere is tilted toward the sun, it is summer in the southern hemisphere and winter in the northern hemisphere. (Principle 1c)

The reasons ice ages occur.
The ice ages were caused by changes in the distribution of solar radiation received over Earth's surface. The path of Earth's orbit is not constant. Variations in Earth's orbital path causes the solar radiation reaching any point on Earth's surface to change. (Principle 1d)

How the amount of energy emitted from the sun (sun's luminosity) changes over time.
The sun's output is not constant. Its luminosity (total energy emitted by the sun) has increased over geologic time, and varies slightly over shorter time scales.

Why recent climate warming has not been caused by increases in the sun's energy output.
The sun's energy output has not changed enough over the last decades to account for the increases in temperatures that have been observed during this same time. (Principle 1e)

Most forms of energy that humans use are derived from solar energy.
Many forms of energy that humans use ultimately derive from solar radiation, such as food, hydrocarbons (such as oil and natural gas), wind energy, hydroelectric power, and of course, solar energy.

Source: Climate Literacy & Energy Awareness Network

Throughout most science education programs and standards, the role of the sun in providing energy to the Earth system is included, but often in a disjointed way. The seasons and their importance in driving seasonal weather patterns and animal migration may be taught in primary school and then not revisited for many years, if at all.

Moreover, students of all ages, including college students and adults, have difficulty understanding what causes the seasons. In addition to the axial tilt, factors that come into play in people's mental models include the belief that Earth orbits the sun in an elongated elliptical path; confusion about the relative size, motion, and distance of the earth from the sun; how light travels; the length of Earth's revolution around the sun; and even the period of rotation. One strategy to mitigate this common misconception is to ensure that the topic is adequately addressed in high school, when students have sufficient background in geometry and physics to grasp the concepts (McCaffrey & Buhr, 2008).

Another common area of confusion that many learners wrestle with is that the atmosphere and the gases that make it up have mass (over 14 pounds per square inch of pressure on top of us at sea level) and momentum. In our everyday lives, we are fish at the bottom of an ocean of air, unaware of the mass that is invisible and feels weightless above us. This confusion is difficult to overcome.

A popular misconception is that recent increases in temperature are due to changes in the sun's incoming energy, rather than increases of greenhouse emissions. This can be addressed by examining records of solar output and comparing them to global temperature records. (See the references section for an article about this.)

Source: Climate Literacy & Energy Awareness Network

Solar radiation is the fundamental energy driving our climate system, and nearly all climatic and biologic processes on Earth are dependent on solar input. Energy from the sun is essential for many processes on Earth including warming of the surface, evaporation, photosynthesis and atmospheric circulation. Thus, examining how the sun fuels different processes on Earth can be a part of many types of science courses. Many of the science concepts relating to this principle can be addressed by encouraging seasonal observations, participating in citizen science programs rooted in the seasons, and periodically revisiting the basics of how the amount and intensity of solar energy affects Earth's climate.

This principle can be taught from a very basic level on upward through the most sophisticated scientific approaches.

Integrating Solutions - The science concepts that relate to solar radiation can be expanded to include solar energy engineering and technology, including solar ovens, passive solar design, solar thermal energy and solar electricity. This can help raise awareness for alternatives to the use of fossil fuel and create a forum for discussions about solutions to climate change that our society can adopt.

Middle school students can begin to understand what solar energy is and how many aspects of life on Earth are dependent on it. Globes and other physical models can be used to show the tilt of Earth's axis and how that affects the distribution of sunlight during different seasons. (see My Angle on Cooling: Effects of Distance and Inclination) Students can learn to visualize the solar system in three dimensions, to understand changes over time, and to begin to understand that energy exists in many forms. Middle school students can also understand the basics of heat transfer and reflectivity and therefore the basics of the Earth's energy budget (see Earth's Energy Cycle - Albedo).

In high school, students are ready to develop a more in-depth understanding of Earth's energy balance. Pathways of energy from the sun and across different aspects of the Earth system can show the transfer of energy (see Effect of the Sun's Energy on the Ocean and Atmosphere). Students can learn about periods of different climate regimes in the past by observing how orbital cycles and ice ages are well correlated. This approach emphasizes the use of graphs with multiple variables and an understanding of long time scales. Students have sufficient geometry and physics background to grasp the concept of the axial tilt being the reason for the season. They will attain a deeper understanding of the cause of the seasons and resulting impacts of the seasons on global climate.

In the introductory undergraduate curriculum, students move on to a more detailed understanding of the various processes controlling the energy balance such as the role of clouds or albedo in controlling the energy that reaches Earth's surface (see Earth's Heat Budget). Milankovitch cycles are commonly used to introduce the concepts of the ice ages. Long term changes in the sun's luminosity can be raised in the "faint young sun" paradox. The concept of uncertainty can be used to emphasize that there are aspects of Earth's history and Earth's climate that are not fully understood.

Source: Climate Literacy & Energy Awareness Network

For more information see this article about the first principle from Encyclopedia of the Earth.

Solar Radiation and the Earth's Albedo - a summary from About.com written for lay audience.

IPCC Fourth Assessment Report 2007, Working Group I: The Physical Basics - Chapter 2: Changes in Atmospheric Constituents and in Radiative Forcing - scientific summary of the latest state of the scientific knowledge on this topic with a special focus on the human impact on the climate system.

Is the sun causing global warming? This page from the Skeptical Science website provides clear answers to common questions and misunderstandings about climate change.

McCaffrey & Buhr, 2008: Clarifying Climate Confusion. - Journal article from Physical Geography about common misconceptions in climate science.

How do we teach about questions with no certain answers? - from a faculty workshop on teaching about the early Earth.

Earth's energy balance since 1950 - brief summary of a recent research article from Physics Today.

Source: Climate Literacy & Energy Awareness Network