The advantage only comes from dual modems or if you're competing with other computers within your home network for bandwidth. Basically, depending on software, you can (theoretically) increase your throughput by up to 100%. The (I think) downside is that often, one will be an intel controller while the other will be a marvell or other controller - I personally wonder how well they play together. An advantage here though is that one type of controller may be more friendly to your modem/ISP than the other.
There is something of an explanation at 11:02 on the video here for the Asus P8Z77-V Premium motherboard which sports two gigabit ports (both Intel in this case). http://www.newegg.com/Product/Product.aspx?Item=N82E168...
Then there is this answer, which I plaguerized from a moderator (bryan) at forums.pcper.com
The big 3 reasons for using dual NICs.
1.) Router, allows you to connect between 2 networks.
2.) Load balancing, where the second NIC picks up excessive traffic from the first.
3.) Redundancy, if one NIC fails the other picks up the connection.
There are a few other uses, but most are very specific in usage.