Plywood is strong because of a property called stiffness. Stiff just means "hard to bend."
If you look closely at a piece of wood, you can see the grain. The grain is formed because of the way wood grows. As you can see, the grain only runs one direction.
If you try to bend a thin piece of wood in the other direction, it will be difficult to bend; it's stiff.
Here's a quick experiment to help you understand!
All you need is a thick piece of paper, like a piece of construction paper.
Cut the paper in half, the short way.
Fold the two pieces up from one end to the other by bending them back and forth like you're making a fan. The folds in the paper are like the grain in wood.
Now, hold one piece of bent paper by the edges and try bending it. You will find that the paper is a lot harder to bend in the direction opposite the fold.
Your paper is stiffer perpendicular to the folds. Wood is stiffer perpendicular grain.
Now, hold your two pieces of paper together so that the folds are perpendicular to each other. You will find that your paper is stiff in both directions!
When we make plywood, we set each layer of veneer so that the grain runs the opposite direction of the previous layer. In this way, we make a relatively thin sheet of wood that is surprisingly strong!
Here's a picture of a cross-section of plywood. You can see that the grain runs in different directions on each layer.
It's also important to realize that glue used to make plywood is very strong! The glued joints can be stronger and stiffer than the original wood!
The plywood-making process