These Pokémon appear at building sites and help out with construction. They always carry squared logs.
– Pokemon White Pokedex
Timburr is always seen carrying that piece of wood. In battle, the timber is animated so that Timburr spins it around once in a while. I’m not sure if that piece of wood would be considered a separate object, or part of the Pokemon. Unlike Farfetch’d and Cubone, who also carry items, there isn’t a “wood” held item for Timburr.
Stat-wise, like a typical fighting type, it has lots of Attack.