Cut meat perpendicular to the direction of its muscle fibers to shorten them and make each bite feel more tender. Slicing parallel to the grain leaves long fibers that your teeth have to tear through lengthwise, so even perfectly cooked meat can feel rubbery. The difference comes from the angle of the cut, not the cooking.
You can see the direction of the grain with the naked eye. Look closely at the surface of raw meat and you can make out fine lines running in the same direction; these are bundles of muscle fibers, which are usually what people mean when they refer to the meat's grain. Hold the knife so it cuts perpendicular to these lines. The lines become even more visible in cooked meat because the fibers contract and separate. If you are unsure, cut a thin slice from a corner of the meat and stretch it from its two ends: if cut parallel to the grain, the slice pulls apart into strands; if cut perpendicular to it, it stays intact and holds together in your hand.
The rule does not matter equally for every cut. In muscles that are used less, such as tenderloin, the fibers are already short and fine, so cutting the wrong way is less noticeable. By contrast, in heavily used muscles such as strip steak, eye of round, brisket, leg cuts, and especially skirt steak, the fibers are thick and long; cutting the wrong way can determine whether the meat is easy to eat. Chicken breast also has fibers running in one direction, so the same rule applies: for schnitzel, slice the breast perpendicular to the grain first, then pound it thin.
The grain direction may not be the same throughout a cut. Large cuts from the leg and shoulder often contain several muscles running in different directions. First separate the muscles along the seams of connective tissue between them, then cut each one perpendicular to its own grain. If you cut through a large leg roast in a single direction from end to end, some slices will inevitably be cut parallel to the grain. Instead of holding the knife perfectly perpendicular, tilting it by about 45° can also help: it creates a wider slice, making a bite feel thinner at the same thickness.
Three details complete the result. For tough cuts, slice thickness should not exceed the 3–5 mm range; a thick slice brings back the long fibers you worked to shorten, undoing the tenderness you gained by cutting against the grain. Let meat rest before cutting it, because juices from meat cut while hot run onto the board and leave the slices dry. The knife should also be sharp: a dull knife tears rather than cuts the fibers, frays the edge of the slice, and drags the meat back and forth on the board, distorting its shape. A long, straight slicing knife makes a cleaner cut here than a chef's knife.