With a rocket fin there are three main issues, strength (will it break under flight loads), stiffness (will it flutter causing the flight loads to go WAY up), and damage tolerance (what happens when it hits the ground).
Without going to far into the math (I would be happy to do that if some one wants), lets hit the strength and stiffness.
Rocket fins can be considered a cantilevered plate, cantilevered because the e fin is not free to rotate at one end. When it flexes, one face is in compression, and one face is in tension. Take a stack of papers, keep them from sliding at the ends and flex them, one side is being pulled tight while the other side is trying to buckle in compression. in the center of the stack of papers, there will be one piece of paper that isn't in tension or compression, this is called the neutral axis of the beam.
The stresses in each piece of paper is proportional to the distance from the neutral axis. The farther away from the neutral axis the higher the stress is. I'm simplifying quite a bit but what the math says is that I can use a weaker material in the center and a stronger material in the outer layers without sacrificing the overall strength of the beam. In a fin, wood is weaker but lighter, fiberglass is stronger but heavier, use the fiberglass on the outer layers where you need them and save the weight and cost in the inner layers.
Stiffness is as important as strength for rocket fins, this gets worse as the speeds go up. Again simplifying the math, there are two factors that are used to determine stiffness of a cantilevered beam (fin), Modulus, how stiff the materials is (the symbol E is used for this), and a geometry factor ( in beams the symbol I is used).
If I change the thickness of my fins without changing the materials, the stiffness (and resistance to flutter) goes up as the square of the thickness, double the thickness the stiffness goes up by 4, triple the thickness and the stiffness goes up by 9. If I use a less stiff material for the middle of my fin (wood) and a more stiff material on the outside (fiberglass) i still get most of the benefits of having a solid fin without the weight or cost.
The best example of this that i pint out to rocket builders is corrugated cardboard like the side of a box. It is really light for its thickness. The box uses a less stiff center, and stiff outer skins. If it was solid it would weight a lot more. When you bend it one skin wants to fail in compression (buckle and (put a slit in the tension face to see this better) the other side wants to fail in tension.
I hope this helps understand what is going on. Tim VanMilligan from Apogee has a good explanation of this in one of his news letters, im sure you can find this on his site.