It may sound like a fancy name, but a French drain is really nothing more than a pipe under the ground. The pipe is used to carry rainwater away from the house or basement. A trench is dug, and filled with gravel. Then a perforated pipe is placed on the gravel and covered with dirt. If you have water standing in your lawn for days after a heavy drain you may want to consider a French drain. Some people have put French drains inside the house in the basement to carry water out of there.
There are many variations of the French drain, sometimes called by another name, but basically the same principal.
You need to check with your local government codes to make sure French drains are allowed in your area. Some places restrict the use of French drains due to the water carrying unwanted materials into the water system.
These articles will give you more information.