It is a common question for new witches.
What is considered “clean” varies from person to person. Some types of energy that one person needs to thrive, another may find painful or toxic. Cleansing is a way to refresh or re-balance your energy to a state where you are able to function at your best. There are standards and traditions in various cultures that are based on norms, but for the practicing witch or mystic, these can be highly personal rituals.
Purification is less personal, and has more to do with ritual purity. Various ceremonies and deities have set or strongly recommended requirements. The practices involved with ensuring that you meet those requirements are purification.
Neither cleansing nor purification have much to do with the physical state of being clean or free of dirt or other foreign materials. For a person whose closest deity is one of athletics, for instance, sweat may be cleansing, and sweating from certain activities may be required purification before some ceremonies. Some cleansing or purification rituals entail being coated in a sacred mud or having sacred smoke blown on you.
Cleansing or purification may be behavioral or dietary as well. Fasting, abstaining from sex, engaging in sacred sex, and giving certain gifts are just a few of the possible activities that can be cleansing or purifying.
In a nutshell, cleansing is relative to the individual, while purification is relative to the ceremony, activity, or deity.