To answer your question directly I don't know all of the details of what a battery pull(essentially a hard reboot of your phone) does but it follows that if you knew what happens when power stops flowing through the phone and what happens on a cold boot of the phone then you know what happens during a battery pull. If it is similiar to a computer then stopping power flow through the machine clears all volatile RAM. The powering on of the device most likely loads the "MBR" of the device and from there loads the OS in it's current configuration. That is a very broad overview and I have not researched the full boot procedure for Android so I am only speculating.
I know the only time I do it is for the same reason I would pull the battery on my old BB and that is because the phone isn't working properly. For me that could mean that the phone is unresponsive or that certain features of the phone or applications on the phone aren't working properly.
I have probably only pulled the battery on my phone a total of 5 times since I got it in July. So it is pretty rare for me to actually have to do that.
Frisco's advice about trying to properly "shutdown" the device first is good also. I haven't experienced any issues with a live battery pull but it's probably better to try these things first.
Also, as Frisco said, there is a button combination you can press while the phone is on and it will reboot the phone for you(soft reset, not factory data reset). The exact combination was posted in the Acclaim section but I tried a quick search for it and couldn't find it. You might try digging that information up again though. If I find it I will post it again.