The Oath Rod is a binding rod that is possessed and used by the White Tower. It is used when raising Accepted to Aes Sedai, upon which they are required to swear the Three Oaths. It makes oaths binding; that is, it is not possible to knowingly break an oath sworn on the Oath Rod unless the rod is used again to release the person from it.
The Black Ajah has found a way to break the Three Oaths while retaining an ageless face. The Black Ajah uses the Oath Rod to remove their Oaths and swear three new Oaths to the Shadow.  One of these Darkfriend Oaths is to "not betray the Great Lord, to keep my secrets until the hour of my death."  Another Oath is to not betray the identity of any Black sisters, although the exact phrasing is unknown.
Seaine Herimon, Pevara Tazanovni, Saerin Asnobar, Yukiri, and Doesine Alwain secretly used the Oath Rod to investigate sisters and force then to reswear the Three Oaths in order to prove they are not a member of the Black Ajah. As part of carrying out this task they tested themselves, Talene Minly and the rebel sisters who were spying on the White Tower sisters.
The day after the Battle of Tar Valon during which she was involuntarily rescued from her White Tower captivity, Egwene "fetched" the Oath Rod from Saerin for two purposes: she wanted to swear the Three Oaths in front of the rebel Sitters and she wanted to use it to ferret out sisters of the Black Ajah who wandered among them. To accomplish the latter she made all rebel sisters reswear the Oaths, but to ensure that members of the Black Ajah did not escape, she kept her possession of the Oath Rod a secret until she was ready to force the confrontation.
Seaine presents to Egwene three possible ways for a Forsaken to circumvent the Oath Rod: using another Oath Rod just after taking the Three Oaths to negate them, sending another woman under the Mirror of Mists to take the Oaths, and using some voice-changing weave to make others hear the words of Oaths instead of the words that were really spoken.
The Oath Rod is the cause of the Aes Sedai agelessness. Although most Aes Sedai believe that the ageless look comes with the ability to channel, the Kin, the Forsaken, the Wise Ones and the damane do not have ageless faces, despite centuries worth of channeling. Egwene herself states to Romanda that the Oath Rod is the cause of agelessness. See also Source:Budapest Q&A, April 2003, close to the end of that long article for confirmation from RJ, himself.