To gnaw is to bite or chew. Your favorite food might be corn on the cob, because you love to gnaw along each row of kernels.
To gnaw also means to deteriorate or wear away as if by gnawing with the teeth. In Arches National Park, the weather has gnawed away at the rocks creating beautiful formations like arches, bridges, and balanced rocks. In this sense, to gnaw can be used even more figuratively. Something might gnaw at the back of your mind — something you were supposed to do, although now you can't quite remember what it was.