What is it called when a singer sings and another repeats the same phrase.?

The term you are looking for is "call and response". Call and response is a musical form in which a leader (the "caller") sings, chants, or plays a phrase of music, and a group (the "responders") repeats it. This form is common in many traditional African and African-American musical styles, such as spirituals, work songs, and blues. It can also be found in other musical traditions around the world, such as Indian classical music and Japanese folk music.