上 here is a resultative complement indicating the beginning or attachment of a feeling. Compare: 喜欢上 (come to like), 迷上 (become obsessed with). Pattern: 爱上 + person/thing.
usage
爱上 implies the onset of love — falling in love. It can be used for people, places, hobbies, or food. For already being in love, use 爱 alone.
