Without going into specifics about TCP/IP routing, gatesways, etc., Windows will pick one of the two connections to be the default one under which your internet traffic will flow through. Connecting the two up at once WILL NOT give you any performance increase.
Now, if you want to investigate details about routing tables, subnet masks, etc, and you have a LAN that you file-share across multiply (i.e. have multiple connections going at once to DIFFERENT clients) and/or connect to the internet with at the same time, you could set it up so that one connection deals with all the traffic from one set of hosts (i.e. half the computers on your LAN), and the other connection works with the other half and/or the internet.
This will require a lot more advance techniques than just plugging it in and running a few Windows Wizards, and even then, I'm not sure that you'd see a lot of performance increase without high-end switching equipmnent, but it is one use of a dual-connection motherboard.