The diagram is what is known as a blackbody diagram. It is a graph showing how much of each wavelength of light an object produces. In a blackbody diagram, it is assumed that the object does not reflect any light, and that all of the light is emanating from it. Blackbodies do not necessarily look black. Stars are pretty good blackbodies, since they are not very reflective.
Image credit: khadley.com
You can think of a blackbody spectrum as being analogous to a collection of bins of colored light bulbs. Each bin holds a different color, and some bins have more bulbs than others. In the above bins, the green bulbs outnumber the other colors. A blackbody spectrum similarly shows the relative abundance of different colors of photons, or different wavelengths of light. The peak wavelength gives a measure of the surface temperature of a star. The shorter the wavelength of the peak wavelength, the higher the average surface temperature of the star.
The PHet site at phet.colorado.edu/en/simulations/category/physics has an interactive simulation regarding blackbody radiation that allows you to see how the peak wavelength varies with the surface temperature.
The above blackbody diagrams depict stars with two different surface temperatures. Notice that the higher temperature star has a shorter peak wavelength. The equation below the image is known as Wien's law, and gives the relationship between the surface temperature of a star and its peak wavelength.
The above graph shows what a real blackbody spectrum of a star looks like. Notice that the edge is very jagged, not a smooth curve. We will learn about the reasons for this when we study our next topic, spectroscopy.
Orion with red giant Betelgeuse. If you look closely, you will see that some of the stars look redder than others and some look bluer. The bluer stars have higher surface temperatures.
Light propagates out from its source in all directions. The light passing through a unit square that is one unit from the source will pass through a square that is four times as large when it is two units from the source. This means that the light gets 1/4 dimmer per unit area. We say that light "goes as" 1/r2.
This plot shows the 1/r2function. Notice that the light falls off very rapidly at first, but then at long distances, the signal tapers off much more gradually. The image below of light propagating out through fog illustrates this property.
Luminosity is how much light a star produces; it can be thought of as how much energy a star generates. Brightness is how bright the star looks to us. The brightness equals the luminosity divided by the surface area of the sphere with a radius at distance d.
You can use the relationship between brightness, luminosity and distance to solve problems involving two stars. Here, star A has brightness BA, luminosity LA and distance dA, with similarly defined quantities for star B.