One good way to look at the difference between ionizing and nonionizing radiation is to imagine a piece of construction paper, suspended magically in the air before you. Now imagine shooting a spitball at the paper. What happens? The spitball doesn't have enough energy to penetrate the paper so it either bounces off, or it sticks. This is how nonionizing radiation behaves when it runs into opposition, say the human body for instance. Our body either reflects the energy, or absorbs it.
Now picture the same piece of construction paper (what color are you picturing, I wonder?). Instead of a spitball, imagine shooting at it with a BB gun. A BB gun puts way more energy into a BB than you're ever going to achieve blowing a spitball from a straw. For this reason, the BB doesn't bounce or stick, but instead passes right on through and continues along its path of travel. This is similar to how ionizing radiation behaves when it comes in contact with your body. In the case of the construction paper, the BB either passes between paper fibers, or it blasts through an individual fiber. In the case of your body, high-energy radiation may pass right on through unobstructed... or it may blow right through one of your cells and slam into a strand of DNA. When it comes time for that cell to divide, it may do so incorrectly, causing a mutation or uncontrolled replication (cancer).
