Color temperature is a way of classifying colors. If we look at a color wheel in it's most basic form with six colors, half the color wheel falls into the warm category the other half is cool.
In this simple color wheel warm colors are the colors of fire- red, orange, yellow. Cool colors are green, blue and purple.
When you consider colors individually, color temperature gets a bit more complex. Each color has hues that could be considered warm or cool.
Take a look at these examples in the green and red color families.
The green that has a more yellow cast is warmer than the green that has bluer cast. The red that has a more orange cast is warmer than the red that has a more a purple cast.
Let's take a closer look at green since it's the color most often associated with landscape painting.
When you compare the two greens below, although they would both be considered yellow-greens, the one on the right is warmer than the one on the left.
Lets add a couple more greens to the mix.
The two greens from the example above are on the right. When compared with the greens on the left, which contain more blue, they're now both on the warm end of the color temperature spectrum. This touches on the concept of color relativity, a complex but important part of color theory. I have two-part series discussing color relativity (here's part one and part two) but in short- it's the notion that colors are affected by the other colors around them- which is why a color that could once be considered cool in the example above, can now be classified as warm in the example below.
The ability to classify color by temperature is necessary in landscape painting because colors generally get cooler as they recede into the distance. Take a look at some of your favorite landscape paintings, do they feel like they recede into the distance? If so, I'll bet it's because the colors get cooler as they move into the background.
I hope this helps increase your understanding of color temperature. If you're interested in more about color theory, check out this post: What Is Value And Why Is It Important.