For Mama, success is growth and placing one's family first.  Her struggling plant is a symbol of this.  Mama feels that if she can keep her family together and satisified, she is successful.

Walter, on the other hand, has an opposing view of success.  He wants to be his own boss, make his own money, and do as he pleases.  He is weary of being emasculated, whether it be by all the women in the house or by being a driver to a white man.  He knows that he is not viewed as the head of the household and feels unsuccessful as a man because of that.  What Walter realizes at the play's end is that being successful for him is being respected and being able to respect himself.