Power Tools
Jointer

Jeff Easter, CC BY 2.0, via Wikimedia Commons
A jointer flattens one face of a board and squares one edge to that flattened face, using a spinning cutterhead set flush with an infeed table slightly lower than the outfeed table -- the board rides down onto the outfeed table's height as it passes over the blades, which is what actually removes twist, cup, and bow rather than just following them. It's the tool that gives every other machine in the shop the two flat, square reference surfaces they all assume already exist.
Why a planer can't do this job
A thickness planer mills a consistent thickness relative to whatever face is already riding on its bed -- it does not flatten anything. Feed a cupped board through a planer and it comes out the same cup, just thinner. Skipping the jointer and hoping a planer will fix a twisted board is the single most common mistake in a new shop, and the reason boards mysteriously won't sit flat or glue up cleanly downstream. See Buying a Jointer for the fuller buying breakdown, including why bed length usually matters more than width.
Bed length over width
Infeed and outfeed table length together determine the longest board a jointer can reliably flatten -- a short bed will happily follow a board's existing curve rather than flattening it out, especially past about four feet. For furniture parts (legs, rails, stiles), bed length is worth prioritizing over width capacity.
Cutterhead type
Straight knives cut cleanly on cooperative, straight grain and cost less. A helical (spiral) cutterhead -- many small indexable carbide inserts instead of one long blade -- handles figured and reversing grain far better, runs quieter, and shrugs off an occasional embedded staple that would nick a straight knife, at a real price premium.
Safety
Keep hands well clear of the cutterhead, use push blocks on shorter or narrower stock instead of bare hands near the blades, and never joint a board short enough that hands would need to pass directly over the cutterhead to feed it through.
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Images

Product: A Powermatic jointer, showing the infeed and outfeed tables and fence — Jeff Easter, CC BY 2.0, via Wikimedia Commons

