Wooden Fences provide (weak) protection to player's character and crops but are easily damaged and destroyed. They are often used around crops as a second protection layer inside the protected area. So the Zombies usually don't hit the fences but when the outer fence layers are broken the crops are still protected for quite some time.
This type of fence is not given for free at the start of the game. While most of them are heavily damaged, they can be used to protect the player, crops and buildings (while zombies do not attack buildings in the game, they will destroy crops and hurt players (shortly).
The fence will have a 'health' of 5, with 1 being the minimum before being destroyed. Fences can be completely restored for 100 cash in the market, including completely demolished (but not removed) fences.