Growth, sunshine and hope are all intertwinded symbols in this play. Mama Lena's little plant is the visual symbol of the meagerness of the family's hope and, ultimately, the family's insistence on that hope.
One of the central challenges for the Younger family in A Raisin in the Sun is finding a way to believe in positive change. They each want to hope for something better, but they each have a hard time believing it's possible.
The only way for the family to cultivate a real hope is to insist on it. This is the one of the final messages of the play.
The struggling plant is symbolic of the Younger family's struggle and it helps to equate the insistence on a hope for something better with an insistence on living.
In the first act, Mama says that she always wanted a garden and this plant is the closest she's ever gotten to having one. She has kept that plant live, along with her hopes for a garden, for years.