Here's a simple example where the certain knowledge of an opponent's hand comes in handy:
Player 1: "Hey, Player 2, I'll trade my wheat for your brick."
Player 2: "I don't have a brick."
Player 1 knows that Player 2 got two bricks and a wood 3 turns ago, and he bought a road. So the one card that's left over is a brick.
Player 1: "OK, I play a knight development card, I move the robber to your plot, and I take your card. Lo and behold, it's a brick!"
