Asha'man is the name given to men who can channel, after they are organized into the Black Tower. The M'Hael is in charge(though under the Dragon Reborn's authority, at least at first), and other ranks include Soldier and Dedicated.
Asha'man can bond women, somewhat like Aes Sedai and their Warder bond, and many of them bond unwilling Aes Sedai sisters. The Asha'man have more control over the woman they have bonded, and can both force them to obey commands and prohibit them from certain actions. The woman bonded can sense the man the same way as a Warder can sense his Aes Sedai.