Geoff Johns likes colors.
It turns out the green energy the Green Lanterns use is just one part of a larger emotional spectrum. Their first encounter with it was through Parallax, a fear demon who harnessed the power of the yellow part of the spectrum. The Qwardians' yellow rings from the antimatter universe harness the same power, and Sinestro teamed up with Parallax and sought out others who relied on fear, forming them into his Sinestro Corps.
The Zamarons then harnessed the power of the violet portion of the spectrum, which represents love, in their Star Sapphires. They're basically selecting those who've lost loved ones and want to spread love through the universe so no one will have to experience that, as well as brainwashing people they capture, like Fatality, into joining them as "rehabilitation."
Ganthet and Sayd left the Guardians of the Universe and harnessed the blue part of the spectrum, hope, to create their Blue Lanterns, whose numbers are very low and whose rings can only work in the presence of Green Lanterns but can also dispel the red plasma that Red Lanterns vomit up and supercharge Green Lantern rings.
Atrocitus, a longtime enemy of the Guardians and Sinestro back when he was a Green Lantern, was really pissed off and killed an old buddy of his, which somehow bound the red portion of the spectrum, rage, to blood. He and his Red Lanterns gained the ability to vomit up plasma that can burn through pretty much anything and drain Green Lantern power rings.
We've just learned that Larfleeze, another ancient enemy of the Guardians, is Agent Orange, tapping into the orange part of the spectrum with his unbridled greed. He's so greedy, in fact, that he kills anyone who comes near him, fearing they'll try to take his orange lantern, and pretty much steals their souls using his power. So the Orange Lanterns are effectively all just constructs that Larfleeze owns.
The Indigo Tribe hasn't been introduced yet, although we've seen pictures. They have staves instead of rings and they represent compassion.
The Black Lanterns have been prophesied by Scar, a rogue Guardian, and are going to be zombie versions of dead established characters like the Superman of Earth-2 and the Martian Manhunter. They'll also be tied to Black Hand somehow, since their symbol is the same as his. Black probably represents death or the end or something like that, but I don't think it's been explicitly stated yet.