Prior to Atta coming of age, the Queen handled all the colony's food production oversight for the Grasshoppers as a form of protection/extortion. Due to an accident caused by Flik the excess food is destroyed before the Grasshoppers arrive and Atta is assumed an incompetent Queen compared to her mother. Despite the Queen's attempts to smooth things over The Grasshoppers place an unreasonable ultimatum on the colony that would leave them unable to gather food for themselves before winter sets in. Though The Queen plays little more than a side character in the film she is still a living Queen and seen by the colony as the center of their universe. The Queen's main contribution from the beginning of the film is strictly in an advisory fashion to her daughter as Atta tries to cope with the stresses and responsibilities of leadership.
At the end of the film, the Queen retires and Atta becomes the new queen with Dot becoming the heir to the throne.
The Queen with her eldest daughter Atta
The Queen and Princess Atta scolding Dot for trying to fly too early, believing she's too young as well her wings are too small.
The Queen with her youngest daughter Dot
The Queen with her daughters
Glenn Close, Carrie Fisher, Kate Mulgrew, and Angela Lansbury were all considered for the role of the Queen before Phyllis Diller was cast.
The Queen is similar to The Queen Ant from Dreamworks' Antz; both are ants, both are the leaders of their colony, both are the mother of the princess of the colony (Atta and Bala), and both later become the mother-in-law of the protagonist (Flik and Z).
In real life, the Queen would be the mother of all the ants in the colony, since the duty of a queen ant in nature is to lay the eggs that will form the colony. So, while Atta and her sister Dot are Princesses as the only daughters of the Queen in A Bug's Life, Atta and Dot would be just two among many other ants of the queen's offspring in real life.