Dowels are used to strengthen joints between two pieces of wood. Irrespective of the direction in which the joint has been made, the two pieces of wood will always be creating tension on the dowel.
This means that when pressure is applied to the surface of either piece of wood, they push down on either end of the dowel, almost as if they are trying to bend it.
Wood is prone to splitting along the grain, so making dowels with grain that runs along their length prevents potential splitting, as tension is only created on horizontal joints (against the grain).
The straighter and more compact the grain, the stronger the dowel will be.