Such analog concepts as "high impedance" and "low impedance" are inappropriate for explaining simple digital configurations like "open collector" to beginners. Instead, simple and clear electrical concepts such as "open switch" and "closed switch" should be used.
A typical example of inappropriate use of "high impedance" are devices with 3-state output. Instead of saying "their outputs go into high impedance state" (whereby beginners look at us with misunderstanding but with "respect":), it would be much better to just say "their outputs disconnect... switch off from the bus". Then they imagine something familiar - an electrical switch. Another example: To turn off the lamp, people say "turn off the switch" and not "set the switch in high impedance state".
So a comparator with an open-collector output stage is a comparator with an internal output switch (n-p-n transistor here) which can be either ON or OFF. One of its terminals (the emitter) is internally connected to ground while the other (the collector) is outed... and it is figuratively named "open collector".
Since the "switch" is connected to ground, it can directly drive loads (LED, relay, motor, etc.) that are connected between the output and positive rail. When the comparator turns-on the "switch", the load will be supplied... and will shine, switch, rotate. Figuratively speaking, the switch "pulls down" the lower end of the load. When the comparator turns-off the switch, the load "pulls up" the upper end of the switch (the open collector).
Only, the input of our load - the microcontroller, is grounded... and it needs to be driven by grounded voltage... by a source. If we connect the open collector to the input, nothing will happen since there is no output voltage... there is only a short connection or open circuit. We have somehow to convert these two states into voltages... and we connect a "pull-up" resistor to the positive rail. Now, when the transistor is ON, the open collector is connected to ground and the input voltage is zero; when the transistor is OFF, the positive supply voltage is applied through the pull-up resistor to the input.
Why the pull-up resistor is not internally connected to the collector? That would be very convenient in this case... there would be no need for all these explanations because everything would be hidden for us. This gives advantages in other applications such as the above where it allows another power supply (higher voltage) to be used. An interesting opportunity is also to connect several open collectors together in the so-called "wired OR"... but this is another topic...
Open-collector circuits also have a major drawback - it is very easy to inadvertently apply +V to the open collector. I remembered for a lifetime what a colleague told me in the early 90s: "If you use an open collector circuit, always someone will connect it to +V".