You haven't given a very detailed information on how your home network is setup.
However with the limited information you have provided, yeah you should be able to take advantage of gigabit.
Like mentioned above, you will need to have sufficient networking hardware that is also capable of delivering a full gigabit service, any hardware or connections that fall below this gigabit spec will become a bottle neck in your LAN.
Most modern/worthwhile modems/routers will have gigabit ports and your computer is fully capable of receiving a gigabit connection via the ethernet port.
Hope that all my ramblings have helped a little...