Distilled water is water that has been boiled into steam and then cooled to become water again. This process removes impurities such as bacteria, salts and heavy metals. The result is water that is pure and does not contain any contaminants.
Purified water is water that has gone through a filtration process to remove impurities. This process does not involve boiling, but instead uses a filter to remove contaminants. Purified water may still contain some impurities, but these are usually at very low levels.