An adze isn't neccessary for survival and is not used commonly. But it is very important for decoration and transportation.
Click on a medium wood a few times to turn it into a plank. An adze can only be used on medium wood.
Adzes can convert medium wood into planks. Planks are useful many things, including boat construction, making furniture, and making looms.
Medium Wood ------> Plank
Similar to most tools created with tool heads, an adze needs an adze head and a medium handle to be created.