Rather than output a signal we often want to provide a current sink. This is common when controlling power to a circuit.
An open-collector output is used to connect one side of the device being controlled to ground. The other side of the device will be connected to power. If you look at the CRICKIT "drive" outputs you will see that this is exactly what they are. You connect the positive side of your device (a high power LED, solenoid, etc) to the 5v connection and the negative side to a drive output.
Electrically the transistor in an open collector configuration acts just like a mechanical on-off switch (except with the benefits listed previously).
In another guide we see another use of open collector connections: when the transistor switch is in its off state, the load is disconnected. One advantage of this is that multiple open collector connections and be tired together and any one can turn on the load independent of the others, operating like an OR gate.
If we add a pull-up resistor instead of a load we get a logic circuit; each transistor functions as a tri-state inverter, together making up a (in this case) 3-input NOR gate. If A, B, and C are all low, none of the transistors are conducting (i.e. on) which means the output is high due to the pull-up resistor. If any on the inputs is high, the corresponding transistor is switched on, connecting the output to ground.
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