To grin very broadly and persistently, especially in a smug, mischievous, or self-satisfied manner. The term was popularized by the character in Lewis Carroll's Alice's Adventures in Wonderland, a cat with the ability to disappear whose wide smile would remain after the rest of it had vanished. I knew he had a prank planned for April Fools' Day when he arrived at work smiling like a Cheshire cat. My dad sat on the porch and smiled like a Cheshire cat as he watched me try to fix the engine all by myself, as I had insisted.