What is the purpose of the Arduino Uno power pins section?

The 5V pin is the output of the on-board 5V regulator. Yes, you are correct that it can be used to power external components which use a 5V connection.

The 3V3 pin is the output of the on-board 3.3V regulator. Same as above as for powering components from it.

The VIN pin is slightly more complicated. If you are not powering it from USB but rather from an external power supply, that supply is directly available on VIN. However, the ATmega328 is still powered from 5V which is available on the 5V pin after being passed through the regulator. So the VIN pin is unregulated (unless your external supply is regulated) and should probably not be used to power external components.

Unfortunately, I believe all the pins on the arduinos are only rated for 40mA. So while your power supply might be able to provide more, if you take it from the power pins you should not draw more than that.

The VIN pin can also used to power the arduino. If you have a battery pack, instead of constructing a plug you can just wire it straight to VIN and ground.