The grain is the way the threads in the fabric goes.
The threads that go across the fabric from selvage to selvage are called the crosswise grain - usually has more stretch than the lengthwise grain.
The threads that are parallel to the selvage are called the lengthwise grain. Usually has the least amount of stretch.
If one goes diagonally, then the grain is on the bias. Usually there is the most stretch when fabric is cut at a 45 degree angle.
This has a fairly clear explanation with illustrations.
http://sewing.about.com/od/beginner1/p/fabricgrain.htm