To lighten, lessen, or relieve, especially physical or mental suffering.
Example:
Cold compresses alleviated the pain of the physical injury, but only time could alleviate the the effect of the insult.
Physical pain or emotional anguish, or a water shortage or traffic congestion, can all be alleviated by providing the appropriate remedy. However, some pain or anguish or shortage or congestion will remain: to alleviate is not to cure.