Simply put, this means diagonal. When fabric is cut diagonally across the grain (at a 45 degree angle) this has couple effects. The most noticeable is that the fabric becomes quite stretchy, which is very useful if you are using it to cover a curved edge. Another effect is that the fabric actually is a bit stronger this way, since you have more woven threads in the same space rather than just vertical and horizontal threads.
Woven fabric of course has vertical and horizontal fibers, woven together to create the fabric. The fibers that run along the selvage is known as the warp, which is also called the “grain” of the fabric. The “cross grain” fibers that run from selvage to selvage are also known as the weft. If you don’t have the benefit of selvage to tell you which way the grain runs, you can tell by pulling on the fabric. When you pull along the weft (selvage to selvage), it will be slightly stretchier than if you pull along the warp (along the selvage).
For more detailed information, follow this link: http://quilting.about.com/od/fabricembellishment/ss/fabric_grain.htm