Easy. The hot black is the incomming power. The black you measured cold carries the current to the fan. The red you measured cold carries the current to the light. The white is the neutral, carrying current back from both the fan and the light. In residential wiring, whites are (almost?) always just all tied together, since you never want to end up with an open neutral.
I had an addition put on and specified to the electrician that I wanted 3 wires to the ceiling box for a fan/light combo. I got just what I expected, a black, red, white and ground wire. Here's where I'm confused. At the switch box, which also contains 3 other switches, all the whites were tied together and for the fan/light combo, I was left with 2 blacks and a red. I assumed two of those would have power and one was common. Checking with my meter, I checked all 3 to ground and all 3 to each other and I could only find power on one black to ground. I bought a combo switch for the fan and the light, which requires a 3rd wire, hooked it up and all is working but I don't understand how. The black w/power went to the fan. How is the light getting power?
thanks,
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