A DIAC looks like a Diode for AC. If we increase the voltage across a DIAC (via a resistor), at a certain voltage it will start to conduct; the voltage across the DIAC becomes 0V. When we then decrease the voltage, the DIAC remains conductive. The DIAC doen't close untile the current ceases. The picture belows may make things more clear.
This DIAC starts to conduct when the supply voltage reaches 32V. Even when the supply voltage becomes less than 32V, the DIAC remains conductive. The DIAC only closes, when the supply voltages becomes 0V. It's obvious that the DIAC also works for negative voltages. Hence, a DIAC doen't have an anode and cathode like a normal diode.