Well...a 32-bit system can only employ up to 4GB of RAM, whereas a 64-bit system hypothetically can employ up to 128 GB (I heard rumors of more).
I think in terms of a MOBO this would mean that there are either 2 or 4 channels on the MOBO. with a 32-bit system you can have 4-1gb sticks, running in dual channel (two sets). Or 2-2gb sticks, if there are only two channels.
If it is a 64-bit system, the MOBO manufacturer is implying that the MOBO is only rated for 4-2bg sticks (most likely).
Does that make any sense?