Row row row your boat?

If someone is singing a song such as 'Row row row your boat...' and keeps singing the rest of the song and after they sing that first verse somebody chimes in with 'row row row your boat' and so on...What is that called?

This is called a canon sung in a round. A canon is a repetition of a melodic phrase, and a round is when the whole song is sung in canon form.

Singing in the round

A 'round'

either a canon or a round