against the grain
Preventing a smooth, level surface from being formed by raising the nap of the wood or causing larger splinters to form ahead of the cutting tool below the cutting surface.
Against the grain: the direction that wrecks your surface
When you plane, sand, or cut wood in the direction opposite to the wood fibres, you are working against the grain. The fibres slope through the wood at angles that vary with the growth rings and the tree's history. A planing tool or saw blade moving against this slope catches and lifts the fibres ahead of the cut, leaving a rougher surface than you would get if you moved the tool in the same direction the fibres run.
The damage takes two forms. First, short fibres ahead of the tool can splinter out and create a torn surface, especially at the edges of boards. This happens because the tool is not slicing the fibre cleanly but peeling it back. Second, even where no obvious splinter forms, the surface becomes fuzzy or raised as the top layer of wood is disturbed rather than severed. This nap, as it is called, catches light and prevents finishes from lying flat.
Direction and depth matter
The grain direction is not always obvious. On quarter-sawn stock, the medullary rays create a distinctive pattern but the fibre direction can still vary. On flat-sawn boards, the growth rings show grain direction in cross-section, but the slope through the thickness of the board may not match what you see on the face. The effect of working against the grain becomes worse the deeper you cut; a plane set to take a thick shaving will tear badly, while a shallow cut might pass almost smoothly even if the direction is poor.
Professional woodworkers learn to read the grain by running a hand over the wood surface or watching how a sharp plane behaves when moved in both directions across a test area. The correct direction is the one that feels smooth and produces fine shavings. On figured wood, where grain direction changes within a single board, you may be forced to work part of it at the best angle you can achieve and accept some fuzzing that will need careful scraping or sanding to remove.
Against the grain is almost unavoidable in crosscutting (cutting across the width of a board), which is why crosscut saw teeth are shaped differently from rip saw teeth. In machine woodworking, feed direction and tool geometry are engineered to minimize damage when the grain direction cannot be controlled, but hand tool work still depends on skill and understanding of wood structure to get a clean result.