An open-drain or open-collector output pin is driven by a single transistor, which pulls the pin to only one voltage (generally, to ground). When the output device is off, the pin is left floating (open, or hi-z).
A common example is an n-channel transistor which pulls the signal to ground when the transistor is on or leaves it open when the transistor is off.
Open-drain refers to such a circuit implemented in FET technologies because the transistor's drain terminal is connected to the output; open-collector means a bipolar transistor's collector is performing the function.
When the transistor is off, the signal can be driven by another device or it can be pulled up or down by a resistor. The resistor prevents an undefined, floating state. (See the related term, hi-z.)