Somewhere, someplace, a long time ago, someone decided to use a piece of wood for leverage. This day was a big day in history. So big it changed the way we looked at wood. Although the person who first used it has fallen into the abyss of lost knowledge/memory, the use of wood for tools is still here today.
And with more and more experemation we discovered quite a few things about using wood as both a tool and as a building product. We found that different woods have different qualities. Some are more ridged, some are more flexible. Some are heavy, some are lights. Some are darker in color, some lighter. And even with all of those differences we started to also find something out, they also share common traits.
When wood growes it is like a really, really, really, tall cone. Each layer increasing both the length of the tree and also the width. Much more on the height than the width. You can see this when you cut the wood into lumber. When you look at the end grain you can see the rings. But that isn't all you can learn from the wood.
It's about the strength of the wood.
We now know which side wants to flex and which side has more stability. Think of a book. Big thick, and strong when you try to flex it from side to side. But you can bend it over without too much effort. Why is that? Because all of the pages are laid out flat.
When you look at a tree think of it the same way. Layers and layers of thin wood all together on the board. The tree wants to be flexible so it doesn't fall down in the wind, and these layers allow movement (sometimes at the top of a tree it could sway 20 feet from side to side without breaking).
But how does this impact the wood that I buy? Well if you want to have something thin yet strong you can use the grain to your advantage. Think of the book analogy. If you don't want to add anything to the neck (graphite or steel rods for strength) then having the grain run 90 degrees as possible will give you the most strength in the smallest amount of volume. The exact is also opposite. If you want to have as much flex as possible without breaking then you need to run flat across the grain.
The 90 degrees would be perfect for a neck, soundboard, bracing. But for acoustic sides, well that would be flat sawn.
Next lets talk about looks and figure.
One of the reasons we fall in love with these instruments isn't just because of how they sound and feel, but also how they look. Flame maple, birdseye, quilt, fiddleback, etc. All of these are influenced heavily by the grain orientation.
Birdseye's are really non-fully formed branches that the tree tried to grow but then gave up on. Now think of that cone tree in the woods. All the branches tend to grow out from the center of the tree. For the piece of lumber to have that killer birdseye look you will need to be as flat to the grain as possible. Same for Quilt.
But if you want to join 2 pieces of wood together and have the glue line be as minimal as possible try Quarter or 90 degrees. The grains will help to keep the joint hidden from view.
It is my hope that this both helps to answer some questions, and maybe start a few.