A linear yard of fabric is a length of fabric that is a yard long. Linear yards only measure length and do not account for the width of the fabric.
Sometimes sewing patterns or instructions will specify if the fabric needs to be a certain square yardage. If so, then measuring by the linear yard is not the best option. This is because the width of the fabric, when a square yardage is specified, also needs to be taken into account. Square yardage is measured by length times width.
For example, the instructions might specify the amount of fabric required is six square yards. If the fabric is only measured out as five linear yards, the width may not be enough to account for the appropriate square yardage. To get six square yards of material, the linear yardage could be three yards, but then the width would have to be at least two yards. If the linear yardage was measured out to be six yards, then one would have to be sure the width of the material was a minimum of one yard. This would also give the person six square yards of material. When in doubt, refer to the old adage of "measure twice, cut once" to avoid any errors.