A reversible key is one that goes in and opens either way up, because its cuts are repeated symmetrically. It does not matter how you put it in: the lock accepts it just the same.
Many dimple keys are reversible, with dimples on both faces, and so are many double-sided keys, with teeth on both edges. To find out whether yours is, look at it head on: if both halves are the same, it almost certainly is.
Its advantage is convenience, especially at night or with your hands full, and the cylinder suffers less because nobody forces the key in upside down. If your current key catches and you are thinking of changing the lock cylinder, ask us about models with a reversible key.