Sang is the past tense of the word sing which means to produce harmonious or musical sounds with one's voice. It can be referred to as a singing that happened in the past.
"I sang for some children at the orphanage."
Sung is the past participle of the verb sing. It can be used to refer a singing action to another action with the help of an auxiliary verb like has or had.
"Michael Jackson had sung his hit single by the time we got to the concert."