Cable has inductance and capacitance, as well as resistance. The combination of a cable's inductive reactance, capacitive reactance and resistance is called its "characteristic impedance." The theory behind it is beyond the scope of this discussion, but a cable's characteristic impedance is independant of its length. A 10-inch piece of Belden 9841 (a recommended type for DMX-512) will have a characteristic impedance of 120 ohms. A 10-mile piece of Belden 9841 will also have a characteristic impedance of 120 ohms.
Characteristic impedance is very important to the behavior of pulses traveling down a cable (and DMX-512 signals are high-speed digital pulses). Pulses don't like to see changes in the characteristic impedance. When the characteristic impedance changes, it causes a part of the pulse to bounce back up the cable in the direction of the source. The bigger the change, the bigger the bounce. If you go from the cable's 120 ohmimpedance to an open circuit (near-infinite impedance), you get a pretty big bounce. The pulses bouncing back from the end of the cable can interfere with the pulses still coming from the controller and cause your lights to misbehave.
As Nephilim said, a terminator is a 120 ohmresistor across the end of the DMX cable. To the pulses getting there from the controller, that resistor looks like another piece of Belden 9841... that goes on forever. They dive into it and never come back.