The short definition for wood grain is the alternating areas of lighter and darker colored wood. Wood grows in concentric layers around the tree beginning with the outer bark, then the cambium, the sapwood, the heartwood, and ending with the pith in the very center of the tree. You can see these layers when you slice through the trunk.
The cambium is the layer of live cells that manufacture the wood for the tree to grow. It generates two different types of wood cells, most of these are long narrow cells running the length of the trunk and those are what give the wood its grain. Because of the way in which trees grow every board has a definite grain. The grain can be made to appear differently depending on how the wood is cut.
Additionally, when a tree is sliced open you will see small depressions called pores. Types of wood with small pores are called closed grain and types of wood with large pores are called open grain.