Fencing is a structure that encloses a yard or area, like the fencing that keeps your dog confined. Another kind of fencing is a sport with long pointy foils that has been popular with Hamlet, Holden Caulfield, and lots of other fancy kids.
You might buy enough fencing to close in your whole back yard — it could be made of wood, metal, or even plastic, and this material can also be called fencing. A completely different kind of fencing is the sport that involves combat with sword-like weapons. Fencing started as military training and a way of settling disputes, but it grew into a sport during the 18th century, and is now even included in the Olympics.