There are 3 reasons that I know of:
1. The motion of the oil circulating into the pump and back thru the drains aids in loosening/disturbing some of the more recently settled depositis sitting in the oil pan, so that they are suspended in the oil and more readily able to be washed out with the oil flow out the drain.
2. Hot oil is thinner, and flows faster & more easily, so it causes the hot sediment in the pan to be thinner and more easily/readily broken up or washed out, almost a solvent effect.
Basically it aids in getting a cleaner change, you can even take it one step further by pouring a bit of fresh oil in with the plug out to rinse the pan. It's not a perfect flush, but it can and does help.

3. The least worrisome and probably least thought about, if you run the engine first, and pump oil to the bearings, it won't drain out and dry up the same as it would overnight. So, when you go to start up, you have a prime of oil in the bearings to help it along for that extended period of time where the new filter element is soaking up fresh oil and taking longer to provide pressure to the engine. Even if you pre prime it, it does help, but still takes a bit longer to pressurize on that first start. Not detrimental to the engine's survival, but it certainly doesn't hurt in extending the engines overall life, and reduces the possiblilty of spinning a dry bearing.

__________________
Chris
64 190D R.I.P.
80 240D W/617 engine -for sale
82 240D -for sale