From the Glossary of The Wheel of Time:

Societies among the Aes Sedai, to which all Aes Sedai belong. They are designated by color; Blue Ajah, Red Ajah, White Ajah, Green Ajah, Brown Ajah, Yellow Ajah, Gray Ajah. Each follows a specific philosophy for the use of the One Power and the purpose of Aes Sedai.

The Red Ajah bends all its energies to finding and gentling men who are attempting to wield the One Power.
The Brown Ajah forsakes involvement with the world and dedicates itself to seeking knowledge.
Blues seek causes.
The Green is the Battle Ajah.
Yellows are healers.
Whites follow logic.
Grays are negotiators.

There are rumors (hotly denied, and not safely mentioned in front of any Aes Sedai) of a Black Ajah, dedicated to serving the Dark One.