Just like the hammer, the wooden plank is a multi-use weapon/tool. The plank is the main component to base fortifcation alongside the nail. The plank can be used as a weapon and can even be upgraded into a nailed plank.
The plank is not recommended for killing any more than 2 zombies. While it has a suitable range, it does almost no damage, and requires 20+ hits to kill a single zombie. However, it does make good crowd control, plowing through zombies with a plank is not a hard task as it has a range of a baseball bat. A plank can be upgraded to a nailed plank, but it is probably a better choice to find a more suitable weapon and to save the plank for fortification.
You can turn a log into a plank with a 1:1 ration if you have an axe and if you are in an area with tons of trees. You can also look around for it, and it is somewhat common in certain areas. In the tutorial mission, you are given 10 planks along with 15 nails and a hammer.
You can make barricades by weilding a hammer and nailing a plank into the window/door. Also, you can craft several building pieces with planks, although it takes quite a bit of planks to build any type of structure.