I've never really been sure what the three pulls on the prop are for, though I do it anyway. One of my instructors tells me it's a waste of time, another goes a funny colour if I don't do it. On my own, I do it for the first flight of the day.
Here's what an old WW2 fighter pilot once told me, and I still remember today:
'On the first pull, check the RPM drop.
On the second pull check the engine oil pressure for excessive drop during the cycle.
On the last pull check for oil pi**ing out between the spinner and cowling.'
The three cycles also circulate warm engine oil through the CSU and actuator for the purpose stated by OC619 above.
MJ