An Essential component of all kinds of stuff. Plus we can chop it to fuel stoves and heaters.
Wood is needed in most of the shelter upgrades, for fuel, to board up and fortify the shelter, and in making certain pieces of equipment. You will need vast quantities of wood to survive the whole length of the siege. Trouble is, it is bulky and difficult to move wood, and that fact is well represented in-game. Wood stacks as high as two units to a slot, half as many as components, but you need several hundred units of it in total. This is a bottleneck I believe was deliberately included for balancing purposes, but is not without its loopholes- Franco, for example. When Franco the Trader arrives at your shelter it is an opportunity to save yourself the effort of carrying things back to your home manually. Trading any finished products you have, like medical supplies if you can spare them, cigarettes, distilled alcohol, etcetera, for mass quantities of wood and components allows you focus on collecting more valuable items instead.
Fuel is also a constant drain on your wood supplies. while books or components can be used instead, books are rare, more expensive and useful to maintain morale and components are more expensive and less efficient than using wood. This drain can really slow your progress a lot, but there are ways to get around that. One, Franco sells fuel fairly often, and again you can trade for things that were easier to carry back home, and your survivors can vandalize locations with a hatchet to turn any unattended furniture into wood and fuel (this is the only way to find fuel in the wild, short of visiting a trader) Fuel stacks four to a slot, double what wood does, meaning if you were planning on turning some wood into fuel anyway you're far better off taking the fuel pre-made from the location in the first place.
Wood and fuel share a notable point- their value seems to double during periods of snowfall. If it's snowing outside, you probably do not want to try to buy either of them. Of course, selling them then becomes viable. A useful exploit related to that value fluctuation is that traders in locations other than your shelter will normally accept wood in trade, so one can essentially pick up wood at the hotel or garage, take it to the attending trader, and transmute it into something simpler to carry. I can recommend using this strategy to fill a stack in your inventory before leaving a place- if you have three vegetables after raiding the garage, put them and anything else you plan on taking home down somewhere, then buy a vegetable with all the extra wood you can't carry home anyway, to top off your stack. It's like free resources... Obviously, this is twice as effective during winter.