Big Bird's Mommy is the mother of Big Bird. Unlike Grover's Mommy, who plays a dynamic role in her son's life, Big Bird's Mommy is a shadowy figure, and seems to have left most of his upbringing to his Granny Bird and aunt Nani Bird.
In Sesame Street episode 0302, Big Bird received a coat in the mail from his mother. Subsequently, however, all known birthday and Christmas presents come from Granny Bird or the residents of Sesame Street.
In Follow That Bird, Big Bird is treated by the Feathered Friends as an orphan, cut off from other birds. This makes some sense if a grandmother is his closest relative, but less so if Big Bird's Mommy is still around. In fact, Big Bird fantasizes about a Bird Family, including a Mommy Bird and Daddy Bird.