What do the colors red and green mean to Dwarves in The Hobbit?
As far as I am aware, the only mention of those colors in regards to the dwarves are at the very beginning of the first chapter 'The Unexpected Party.' It is said that Dwalin has a dark green hood, Balin has a scarlet hood, and Bombur (I assume it is his, rather than either Bofur's or Bifur's, due to the order they and the cloaks are mentioned in) has a pale green hood. Blue seems to be an important color because it is worn by Thorin, Fili, and Kili, all of whom belong to the royal line. Of course, Dwalin and Balin, who are brothers (Balin is the eldest), are also descended from the royal house of Durin; if you exclude Bombur's pale green as being different and separate from the dark green of Dwalin's hood, you could take it to mean that blue, green, and red are worn by those who are in Durin's line. Of course, that is something quite big to just ignore.
One culture that does place importance on color is the Istari, or the wizards. They had Saruman the White (who becomes Saruman of Many Colors after becoming evil), Gandalf the Grey (who becomes Gandalf the White after being killed by the Balrog), Radagast the Brown, Morinehtar the Blue, and Romestamo the Blue. For them, it seems that the order of importance is the order I've just put them in, though being "of Many Colors" probably pushes Saruman out of the order entirely.