What does it mean to cut meat against the grain? First things first, the "grain" of the meat refers to the direction of its muscle fibers. So cutting against the grain means cutting across those parallel fibers to make the meat easier to chew.
How do you know what direction to cut? Examine the meat's surface and find the direction of the muscle strands. Place your knife perpendicular to those strands, then slice. This is easiest to do with cuts like flank steak or tenderloin.