OK- you currently have a dual core processor, this IS two processors, it has two complete CPU each with their own blob of cache memory on chip. It also has the memory controller on-chip as well, so access to the RAM, HDD etc is super fast. Becuase its a 64bit processor the memory busses into and out of the chip is 128 bits wide each way, so with 32 bit code you would have twice the data bandwith compared to a 32bit P4 core whch has a 64 bit wide path each way and the memory controller is in the northbridge chip. You would also be runnig dual channel RAM I think so for example one CPU can be reading from the RAM while the other is writng to it and at 4 32 Bit words per cycle each way its pretty fast.
If you were to buy a dual socket mother board and run two processors you would have to by an expensive server type motherboard and 2 processors, which would be more expensive than your current setup. The only adavntage would be a minor increase in memory access speed due to two controllers, one in each chip, but the processing speed would not be any faster with the same CPU frequency. The server boards may only take server type processors like opterons etc which are more expensive than equivalent speed Athlon 64 chips because they are tested and rated for higher reliability. The server board may also require Error checking Registered server RAM, whick is reliable as hell and a bit faster, but 2-3 times the cost of ordinary DDR400 Ram. It also has a higer latency, or access time due to the extra circuitry the signals have to go through on the way into or out of memory.
You may be lucky and find a MB that takes two ordinary CPUs, RAM etc.
With your current setup there would be little point in going for two separte Processors, unless you put 2 dual core Athlon X2s in- mmmmm 4 cores.