Hardwood is one of the most important resources in the the game because it (together with Feathers) is needed to craft Arrows. Luckily it is rather abundant in the Siberian Wilderness as well as the Peruvian Jungle.
Depending on the Difficulty settings one has chosen (starting with Survivor in Rise of the Tomb Raider, or normal Exploration Difficulty in Shadow of the Tomb Raider), hardwood is also needed to light the fire at a newly discovered Base Camp; this is also true in the Endurance Mode.
Rise of the Tomb Raider
Upgradable by Hardwood
Shadow of the Tomb Raider
Lara can carry up to 35 pieces of hardwood without upgrading her carrying capacity.