Why is it important to know if a color is warm or cool? There are many reasons!
Let's talk about warm and cool as it pertains to paintings. As a general rule warm colors appear to advance and cool colors seem to recede. (Notice that the above painting is an exception- there's always an exception.)
Every color has a warm or cool character. A red that leans toward orange is more warm (red, yellow, oranges are warmer). A red that leans toward violet or blue is cool (blues, greens and violets on the color wheel are cool).
When an artist paints a scene, if the warm colors are placed in the background the sense of depth is challenged a bit. Look at this beach scene and notice how the water is moved from green to blue behind the wave on the left. The green is cool but I moved it to a warmer green on the wave by adding a bit more yellow to it. This green helps the wave advance. Then behind it I placed a blue to immediately create depth because the blue color is more relaxing, more calm and has less energy. The colors in sunlight that are warmer, are higher in energy. They seem to some people as a bit louder. I think of them as being more energetic or enthusiastic.
In this wave painting I've abstracted some areas while in other areas I painted a bit more realistically to create a balance between the logical (details & realistic) and emotional (colorful & abstract) mind. Balancing the warm and cool colors, the logical and the intuitive and the masculine and feminine energies is my goal when painting and living. What is your goal when collecting or creating art?