To give you an idea what long grain means, I have cut and pasted from an article which can explain better than I can, I hope this will give you a better understanding:
Grain direction is an important consideration in printing processes such as sheetfed offset lithography (in particular multiple-color work), especially in connection with dimensional stability, or how well a particular sheet of paper will retain its original length and width upon exposure to moisture. When paper fibers absorb water, they will expand in width, but not in length. Therefore, the direction of greater dimensional change will be in the cross-grain direction. Long-grain paper is generally preferred to short-grain paper for offset lithography, as the total dimensional change due to moisture will be less if the expansion is in the shorter dimension. This is an important consideration when separate colors in multiple-color jobs need to align properly. In some cases, however (primarily in black-and-white and single-color jobs), short-grain paper is preferred, as register is not a concern. In addition, since paper is stronger against the grain, paper that is fed into the press against its grain will be less likely to suffer from structural deformities such as curling, stretching, or waffling as a result of tensile forces. When pages are to be bound, as in books and catalogs, the grain should be parallel to the binding edge. Pages bound with the grain perpendicular to the binding edge do not lie flat or turn easily.