A French drain is often added to property where the natural slope isn't enough to move excess storm water off the property.   Some texts reference these systems having been invented in France.  However, our use really goes back to those popularized by Henry Flagg French.   French drains are usually buried under the lawn. They usually rely upon a corrugated tube with perforated holes at the top.  Such a buried tube allows excess water to be quickly moved away from ponding on a property.   A smoother tube is preferred as water tends to be left over in the curves of the corrugated pipe.  This can create a breeding ground for mosquitoes over time.  They are also more difficult to clean.
Another type of French drain is a concrete trough dug into the ground and covered with a metal grating system.  This is more obvious to the observer, but can be very efficient and much easier to clean.  We have more details about drainage solutions here.