A tuber is a specially-designed storage organ that grows underground from the stem of some plants. They allow the plants to store nutrients through the winter, and are very commonly eaten by people for those delicious nutrients.
Far and away the most common tuber is the potato. They are ubiquitous and delicious. Another somewhat popular one is the yam. Note that this is different from the sweet potato, which actually is unlike the potato and is just a tuberous root.