Krishna is the incarnation of Lord Vishnu and Radha is of Goddess Lakshmi. Once a devotee wishes to Lord Vishnu to get Lakshmi as his wife. He did several years of Tapasya and then Lord Vishnu blessed him and gave what he demanded. Lord Vishnu said Lakshmi will be his wife in his next birth. So Goddess Lakshmi was incarnated in the form of Radha to complete Lord Vishnu's boon.