"你吃了吗？" (Have you eaten?) is a traditional Chinese greeting, similar to "How are you?" — reflecting how central food is to Chinese culture. You can just reply "吃了" even if you haven't.
usage
吃 appears in many common collocations: 吃饭 (eat a meal), 吃早饭 (eat breakfast), 吃药 (take medicine), 吃亏 (suffer a loss). In chess, 吃 means to capture a piece.
