Some cuts of meat have distinct lines in them. Flank steak, skirt steak, brisket and London broil are good examples. These long lines are fibers running through the meat, and they are difficult to chew through. These cuts of meat are usually sliced (before or after cooking) in a way that fibers are cut through. In this way, the meat becomes more tender and easy to eat.
Look carefully at the flank steak on the grill in the picture. Lines are running from right to left down the length of the steak. If you slice this steak in the same direction as those lines, you'll have to chew through the fibers. Whereas if you cut across the lines, the knife will have already done that work. Think of it similarly to slicing a stalk of celery. The strings are less likely to get caught in your teeth if you cut those strings into smaller lengths.
When slicing this type of meat, it is often recommended to slice thinly at a 45-degree angle. If the steak is thin (such as flank steak), I don't worry about the angle, though it is more elegant in the angled strips.
