Lorna Goodison's "I am Becoming My Mother" is a beautiful, image-heavy, celebratory poem that describes how much the speaker has in common with her mother, how they share specific traits as well as a sense of belonging together in a powerful, long line of females. Although we can't assume automatically that authors are speaking the words of their poems directly, in this case, we can: Goodison herself has said that the poem is about her and her own mother.
Here's the second stanza:
My mother raises rare blooms
and waters them with tea
her birth waters sang like rivers
my mother is now me
The line in question is the third one: "her birth waters sang like rivers." It's a rich one, very open to interpretation!
In one sense, this line could mean that when the speaker's mother gave birth to her, the rush of the mother's fluids that had nourished the baby was like a powerful song of nature.
In another sense, the line could mean that, like a singing river, the speaker and her mother (and the rest of their female ancestors) are connected in a long, flowing, beautiful line of femininity and humanity.
In a third interpretation, you could read the line as a reference to the family's home country of Jamaica, as an indication that the land or the other people living there were joyous when the speaker's mother was born. (By calling a place your "birth waters," you might mean it's the place where you were born, the place that continues to nurture you physically and spiritually.)
Finally, you can interpret the whole stanza to mean that the speaker's mother raised wonderful children ("rare blooms") and that every time she gave birth to a child, it was a joyous, almost musical occasion. If you favor this interpretation, you'll be interested to know that Goodison had eight siblings!